I would definitely argue the American Revolution fit's the OP's criteria. OP does mention the colonial militias in the comments, but the minutemen were very much seen as a civilian militia that was expected to provide their own arms and uniforms and were very explicitly civilians first, not soldiers. They also lacked the discipline and organization of a professional army, which was a big handicap until people like von Steuben were able to drill the Continental Army into shape. Militiamen would often show up and leave at a moment's notice, and there was no long-term cohesion. They were much closer to "a bunch of locals with guns" than a professional army.

By contrast the actual professional soldiers in the colonies on the eve of the American Revolution were the British "redcoats", who were more or less loyal to the British Parliament. There were a few cases where British soldiers defected to the American side, but it was rare because there was very little the colonies could offer a prospective defector. Some of the answers to this question on Quora give some reasons as to why there were so few defections from the Crown to the continental Army, but there were some, like Richard Montgomery and Horatio Gates. Additionally most of the British soldiers were shipped in from overseas so they had very little colonial sympathies. Some of the American militia served in the Seven Years' War, but they served as part of local militias instead of as part of the main British army. For example, George Washington served as a local guide and later a local militia leader during the Seven Years' War, but he didn't seem to serve as an actual soldier in the British Army proper.

Overall, it's very different from the stereotypical depiction of revolutions where the heads of the state's official army decide to seize power or defect/abet an existing revolutionary movement (but not historically unique, as other have pointed out here). The thing that makes the American Revolution a bit more distinct is you had very few with split loyalties between the colonies and the Crown among the British soldiers, so defection of military officers to the rebel forces was a much less important factor than in most revolutions.

Another revolution to consider is Haiti 1793-1804.

Although L'Ouverture allies his former slave army with the Spanish military and then the French, he is eventually betrayed in 1802. From 1802-1804 it's just the revolutionary forces vs. the military of Napoleon's Republic.

In October 1802, Revolutionary leaders, including Dessalines and Christophe, at last defect from the French... A new revolutionary army forms with mostly black officers and rank-and-file soldiers. Blacks and mulattoes begin to form a national identity around their common goal of expelling the French.

-Brown University Library

Of course, the revolutionary army probably wouldn't have stood a chance without yellow fever devastating the European forces, but I think this revolution qualifies.

Abdication of Napoleon in both 1814 and 1815 was forced by the Paris mob, led by disloyal civilians such as Talleyrand and Fouché, despite the unquestioned loyalty of the French Army.

Nicaragua 1979

The overthrow of the Samoza regime and the National Guard (as the Nicaraguan military was then known) by the Sandinista National Liberation Front in 1979 during the Nicaraguan Revolution seems to qualify.

With an estimated death toll of at least 30,000 and numerous clashes between students, guerrillas and the National Guard, it certainly wasn't peaceful.

Cuba 1959

Fidel Castro's rebel army completed the overthrow of the Cuban president Fulgencio Batista when the latter fled Cuba on January 1st, 1959 after an estimated 5,000+ combat-related Cubans had been killed. Castro's rebel army comprised people of various backgrounds and had widespread support among the general population.

Although the Cuban army greatly outnumbered Castro's insurgents and was better (though not well) armed, it was poorly led, corrupt and alienated the people. Ultimately,

While the Army was initially effective against the insurgents it proved incapable of modifying its tactics to deal with a changing political situation.

Source: Major Ricardo J.Blanco, Counter-Insurgency in Cuba: Why Did Batista Fail? (Master's thesis, 1994)

Also, by alienating the people,

The insurgents were able to turn this to their advantage with effective propaganda and consistent, fair treatment of the public.

Source: Blanco

The central problem in the theory presented in the question is this:

According to their reasoning, the leaders of the military control the military, and thus have enough firepower to defeat any popular uprising.

Well, the 'leaders' do not always 'control' the military on all its levels. It's an idealisation. The average grunt sometimes thinks for himself.
And when a revolutionary struggle, sometimes after quite a long time, seems to be successful, then quite often the military establishment switches sides.
So, this would mean that only a majority of generals count, if the are stubborn enough to continue fighting for the losing side in a Ragnarök?

The peripheral problem with that theory is that it's unclear what really constitutes 'a revolution'. And when is that 'over'?

The Red October, the Russian Revolution was decidedly against the established military leaders. Those were then killed, fled or reformed in the "Whites". According to the criteria set forth this is only gradually different from the February revolution?

When did that revolution end? In 1917/18? in 1922? Or was it successful at all? Given that Stalinism might be an objection to that. Or was it ultimately unsuccessful, looking at the world after 1991?

Mao's long march is the first that then comes to mind, going against Chiang Kai-Shek's official government and forces. Or is this all just factions in a long civil war?

Then the East German counter-revolution was quite peacefully victorious against the geriatric leadership. At first the military and militarised police were very much preparing to suppress it the traditional way, but then lacked decisiveness and felt unsupported from the Soviet side, effectually thinking "then screw it all".

In the weeks from the start of October until the opening of the border in November, it was completely unclear to both those affected and those watching on, whether the GDR leadership would seek to save itself using the "Chinese solution". As a precaution, the national army of the GDR was placed on high combat readiness during 6–9 October.
The SED wanted the jubilee celebrations on 7 October 1989 to pass as smoothly as possible. They therefore allowed the speedy deportation of the embassy refugees and also permitted their family members to follow.

However, problems had already arisen during the run-up to the day: Rejected invites from guests, those selected to receive honors stayed away and all sorts of abandoned events. On the day of the anniversary, western journalists were denied entry to the country. Here and there, anti-celebratory events took place. At peace prayers, the 40th anniversary celebrations were partly critically mentioned; in Gotha, for example, forty candles were extinguished as a symbol of extinguished hope. Gorbachev, who had traveled for the celebrations, saw the writing on the wall for the SED regime.

Aside from the official celebrations, there were also many demonstrations of protest across the GDR: From protesters who congregated on the 7th of each month at the Alexanderplatz in Berlin to remember the electoral fraud, a protest march was formed that headed toward the Palace of the Republic, where the main celebratory banquet was taking place. The growing crowd of around 3,000 made its presence known with chants of "Gorbi, Gorbi", "no violence" and "democracy - now or never". However, under pressure from the security forces guarding the venue, the crowd could not directly reach it and instead swerved away to Prenzlauer Berg, where over 2,000 people were at the time gathered in the Gethsemane Church.

In total, 1,200 arrests were made, including people completely uninvolved. The majority were released from custody within 24 hours but reported being beaten, kicked, spat at or denied usage of a toilet. Unlike the other protests across the GDR, the events in East Berlin were directly reported in western media.

Is the First secessio plebis a revolution? If it's a 'yes', where to put the military in this struggle, at all?

The "Iranian Revolution" seems to tick all boxes:

Demonstrations against the Shah commenced in October 1977, developing into a campaign of civil resistance that included both secular and religious elements, and which intensified in January 1978. Between August and December 1978, strikes and demonstrations paralyzed the country. The Shah left Iran for exile on 16 January 1979, as the last Persian monarch, leaving his duties to a regency council and Shapour Bakhtiar who was an opposition-based prime minister. Ayatollah Khomeini was invited back to Iran by the government, and returned to Tehran to a greeting by several million Iranians. The royal reign collapsed shortly after on 11 February when guerrillas and rebel troops overwhelmed troops loyal to the Shah in armed street fighting, bringing Khomeini to official power. Iran voted by national referendum to become an Islamic republic on 1 April 1979 and to formulate and approve a new theocratic-republican constitution whereby Khomeini became Supreme Leader of the country in December 1979.

The revolution was unusual for the surprise it created throughout the world: it lacked many of the customary causes of revolution (defeat at war, a financial crisis, peasant rebellion, or disgruntled military), occurred in a nation that was experiencing relative prosperity, produced profound change at great speed, was massively popular, resulted in the exile of many Iranians, and replaced a pro-Western authoritarian monarchy with an anti-Western totalitarian theocracy based on the concept of Guardianship of the Islamic Jurists (or velayat-e faqih). It was a relatively non-violent revolution, and it helped to redefine the meaning and practice of modern revolutions (although there was violence in its aftermath).

Under the conditions set forth, how to classify the Arab spring events of 2011 in Tunisia, Egypt and especially Libya? Violent citizens did overthrow their leaders who had the support of their military leaders. But was that any success at all?

The People Power Revolution:

involved over two million Filipino civilians, as well as several political and military groups, and religious groups led by Cardinal Jaime Sin, the Archbishop of Manila, along with Catholic Bishops' Conference of the Philippines President Cardinal Ricardo Vidal, the Archbishop of Cebu. The protests, fueled by the resistance and opposition from years of governance by President Marcos and his cronies, culminated with the absolute rule and his family fleeing Malacañang Palace to exile in Hawaii. Ninoy Aquino's widow, Corazon Aquino, was immediately installed as the eleventh President as a result of the revolution.

If we then look at the government that ruled over the 13 colonies we see that "the military" was also British. Depending on how this narrative is told, we see non-military citizens fight that military-backed government, and actually overthrow it through force. Citizens, including citizens formerly in the army, fight the government. Those civilians did form an insurgency which grew its own military over time and eventually defeats the military-backed government.

Instead of listing ever more examples of these presumed patterns, let's read again:

Most analyses of coups focus on the involvement of the military in this process (Finer 1962; Feaver 2003). Coups occur when military elites receive relatively few rewards, which the literature conceptualizes in terms of low military spending, the absence of graft for the military, or economic shocks (Belkin and Schofer 2003; Besley and Robinson 2010; Collier and Hoeffler 2007; Gallego and Pitchik 2004; Londregan and Poole 1990; J. Powell 2012). Acemoglu and Robinson (2001) pro- vide an influential class-based model of sequential coups and revolutions in which income inequality drives institutional change. According to Meltzer and Richard’s (1981) model, in democracies, the more numerous poor tax the rich. Should shocks provide the rich with an opportunity for a coup, they are most incentivized to do so when there is large income inequality. Similarly, inequality leads the poor to want to rebel against autocracy should they get the opportunity.

While the romantic version of a revolution involves the people storming the barricades, in reality, many revolutions succeed because elites (and military elites in particular) desert the regime (Myeserson, 2008). When the masses rebel, coalition members choose whether to suppress the rebellion or sit on their hands. If coalition members desert the regime, then the revolution succeeds and the masses, selectors, and former coalition members all receive payoff y.

In 1979, the Shah of Iran fell because the military was no longer willing to suppress the masses. Similar fates befell Ferdinand Marcos in the Philippines in 1986 and Mobuto Sese Seko in Zaire in 1997. Each had the same political problem; they were mortally ill and their supporters deserted them, refusing to put down rebellion. Supporters are only prepared to suppress the masses when their interests are served by preserving the current regime. When the leader is sick, she can no longer promise access to future private goods.
_{Bruce Bueno de Mesquita & Alastair Smith: "Political Succession: A Model of Coups, Revolution, Purges, and Everyday Politics", Journal of Conflict Resolution, Vol 61, Issue 4, 2017, 1-37, online: September, 2015.}

That makes the initial "assertion"

Various historical and political theorists (for instance, Bruce Bueno de Mesquita) have asserted that the support, or, at most, the abstention of a country's military is necessary for a successful revolution.

something like a misreading prompting an attempt to disprove a truism. If a ruler's military deserts him after the first signs of stressful struggle he wants suppressed, it should be clear that it's a lost cause for the ruler from the start. Having the established military on your side is in any case a plus. Winning them over in the course of events is not bad either. That means it is perhaps sufficient but not necessary.

Myerson explains these insights in their simplified form as follows:

First and foremost, a successful leader needs a reputation for reliably rewarding his supporters. To compete for power under any political system, a leader needs the active voluntary support of many individuals, and these supporters must be motivated by some expectation of future reward in the event of their success. But when rivals have been defeated, a ruler may be able to enjoy the fruits of power without such broad support, and so an established ruler may be tempted to ignore the claims of past supporters. So the credibility of a leader's promises may be doubted if there is noth ing that constrains rulers to fulfill their past promises (see North 1993; Root 1989; and Shepsle 1991). Thus, leaders who are subject to constitutional constraints can have a competitive advantage over pure abso lutists, whose sovereign freedom after winning power may reduce their ability to credibly recruit supporters beforehand.

According to Xenophon, Cyrus established himself as a great political leader by cultivating a reputation for generously rewarding his captains after victory. So the essential point of his story is that a successful leader needs a reputation for reliably rewarding those who work to put him in power.

Our model is only a simplified abstraction of real political systems, but it offers insights into the nature of political leadership that can be applied to better understand the complex political systems of real life. Our main result, that a successful leader's power must be based on his reputation in a forum where supporters can communicate grievances, implies an essential generalization of the traditional English doctrine that sovereignty is held, not by a king alone, but by a king in parliament. The term parliament itself comes from a word for communication.

Competition for leadership within a political party is rarely regulated by external laws, and a successful party leader needs active supporters within the party to whom he may be bound only by the kind of personal constitution that has been discussed here. Of course the larger constraints of a democratic constitution should limit a successful leader's ability to divert public resources to reward his active supporters. But the voters' evaluation of a polit ical leader should take account of the circle of active supporters around him, as his relationship of trust with these supporters is a primary political commitment for the leader.
_{Roger B. Myerson: "The Autocrat's Credibility Problem and Foundations of the Constitutional State", The American Political Science Review, Vol. 102, No. 1 (Feb., 2008), pp. 125-139.}