St. Augustine, in his final book, the book of his retractions, he says: "How many rascals are saved by being baptized on their deathbeds? And how many sincere catechumens die unbaptized, and are thus lost forever! ...When we shall have come into the sight of God, we shall behold the equity of His justice. At that time, no one will say: Why did He help this one and not that one? Why was this man led by God‘s direction to be baptized, while that man, though he lived properly as a catechumen, was killed in a sudden disaster and not baptized? Look for rewards, and you will find nothing but punishments! …For of what use would repentance be, even before Baptism, if Baptism did not follow? ...No matter what progress a catechumen may make, he still carries the burden of iniquity, and it is not taken away until he has been baptized."
The jist of it is that he states as if it were fact that there certainly are death bed conversions, yet he is very specific in that he says that those who get baptized, then die are saved.
If salvation in the last nano-second of the life of an infidel was a possibility, then common sense dictates that St. Augustine certainly didn't think so because if sincere catechumens are lost forever, then certainly a person who doesn't even know how to make an act of perfect contrition stands no chance whatsoever.