When we read Cicero, we find that even the Romans themselves (or at least their most famous orator and politician) think that the Roman state ceased to exist in any meaningful sense long before the time of Christ (Cicero himself died before Christ was even born).
Augustine ends this chapter by promising to discuss more the fact that "Rome was never a republic, because true justice never had a place in it."
To be fair, "I grant there was a republic of a certain kind, and certainly much better administered by the more ancient Romans than by their modern representatives." That is, we can look at Rome and recognize the form of government that is generally called a 'republic' by the world, and we can admit that the Romans of the 3rd century BC and earlier did a better job of managing the state than the Romans of the 1st century BC. "But the fact is, true justice has no existence save in that republic whose founder and ruler is Christ, if at least any choose to call this a republic; and indeed we cannot deny that it is the people's weal."
If the definition of a republic is that it is governed by justice exercised for the common good (as Cicero would rightly argue), then we can say that Rome was never a republic in anything more than semantics (nor, for that matter, has America ever been one), and that only the city of God can make the exalted claim to being a state run justly and for the common good.
Again, even before the coming of Christ the pagan 'gods' repeatedly failed to save the city of Rome either from its immorality or from invasion and destruction. Placing the blame on Christians for something that was an established pattern long before Jesus was even born simply demonstrates how deceived the Romans are about even the simplest matters of theology and history.