Why did St. Monica defer St. Augustine's baptism?

Theology of Baptism in the North African Early Church

Although infant baptism was practiced in the early church prior to Augustine (b. AD 354), there seemed to be a movement against infant baptism at least in North Africa which may have started as early as from the period of Tertullian (Carthage, d. AD 220).

The following quote is from a 2000 MA Theological Studies Thesis "Tertullian and the Catechumenate: An Inquiry into Tertullian's Justification for the North African Catechumenate in the Early Third Century" for George Fox Evangelical Seminary by Loren Kerns (I added formatting):

In conclusion, the answer to the thesis question, why did the Christians in third century North Africa believe that it was important for converts to wait, comes in several parts. This paper will seek to demonstrate that from Tertullian's viewpoint, the existence of the catechumenate was justified on the basis of a matrix of theological and pastoral concerns.

1. First, his theological understanding of baptism as a bilateral covenant between God and humanity, and his view of repentance as necessary in order for baptism to be efficacious, required pre-baptismal preparation.
2. Second, the implicit pastoral concerns arising out of a desire to ensure genuine repentance prompted Tertullian to counsel deferring baptism.
3. Third, the post-baptismal commitments implied by his theology of baptism resulted in a desire to postpone baptism for the catechumens until they were ready to live it out.

Finally, the urgent and zealous flavor of his pastoral concerns for the catechumens were deeply shaped by the hostile environment facing North African Christians, bolstering a call to greater commitment.

From the Thesis's conclusion (emphasis mine):

Tertullian's vision for the catechumenate hinged on his emphasis of human responsibility. Sin was the sole result of human rebellion, and the will was the culprit. Although the Fall had obscured the image of God in humanity, Tertullian contended that it had not destroyed the will's freedom. Adam had chosen to rebel against God in Paradise, and now it was his responsibility to return to God. Thus, repentance, sorrow for sin, fasting, separation from all idolatry, and embracing the Church with its creeds and discipline were necessary to merit the grace of baptism. He knew nothing of the Augustinian ideas of predestination, total depravity and irresistible grace. Grace really depended on human response, and the catechumenate sought to ensure that it happened.

For more on the early church belief of baptism as regenerative sacrament, the logic of postponing baptism (for infant, as well as for adult), and possible connection of the postponement to 1) the Novatian Controversy (who denied penance to mortal sinners) and/or 2) the severity of penance for post-baptismal mortal sinners, see the blog article Does Tertullian Reject Infant Baptism? by Joe Heschmeyer.

Monica, Augustine's infant catechumen & boyhood illness, Baptism

The following quote is from Augnet's page on Augustine's childhood:

Infant Baptism

Monica instructed Augustine in the Christian religion and taught him how to pray. As a child, blessed salt was placed on his tongue. He thus formally became a catechumen, i.e., he was enrolled in the process of baptismal preparation. Once while still of school age, he became dangerously ill. He desired baptism and his mother prepared everything for the ceremony. Then suddenly he grew better, and his baptism was put off.

His baptism was deferred lest he should stain his baptismal innocence by falling into sin before reaching maturity (which is exactly what happened). This was an example of the practice of that era to defer baptism for fear that the recipient would fall into sin before coming fully to realise the great importance of the Sacrament. As a bishop in his later years, Augustine denounced this custom of deferring Baptism as being very ill advised. He preached strongly against it.

A Wycliffe College course notes page "Augustine's Life: An Outline" has this about when Monica almost had Augustine baptized when he became gravely ill as a boy (emphasis mine):

Although Monica, his mother, had tried to raise Augustine to be a Christian, enrolling him as a catechumen as a child, Augustine himself did not seem to have any natural interest or inclination in that direction. As a boy, he became gravely ill, whereupon his mother arranged for him to be baptized. When he recovered, though, his baptism was put off. Baptism was a rite popularly believed best administered at the point of death so that one might not thereafter fall from the state of grace into which he/she was baptized. For this reason, namely Monica's concern that Augustine's sins would be more grievous after his baptism than without it, the act went undone. ...

Conclusion

If Tertullian's theology of baptism and/or the severity of penance for post-baptismal mortal sin continued to Monica's day in the North African Early Church, it's not surprising that:

• Monica didn't baptize Augustine when he was a baby (AD 354) but she was determined to raise Augustine in the faith as though he was already a catechumen (from your quote: "In his infancy she had ranked him among the catechumens").
• When the 7 year old Augustine became gravely ill it made sense to prepare baptism as part of the last rite, but because the North African church apparently believed baptism should better follow a rigorous and mature faith, this preparation was undone after Augustine recovered from the illness.

Another possible explanation that is sometimes mentioned was that Patricius, Augustine's pagan father, forbid it. As for why St. Monica married a pagan, it was an arranged marriage and if she was married around AD 350 we should remember that it was mere decades from the Edict of Milan (AD 313) before which Christianity was still illegal and had just endured one of the worst persecutions that ran for about 10 years thus limiting the supply of eligible bachelors, which possibly made the church more relaxed in allowing mixed marriages. Regardless, St. Monica's piety was demonstrated by her endurance to practice her faith and her solicitude (and later success) for the conversion of both her son and her husband.