To briefly summarize, in Calvinism, the central point of the doctrine of the "perseverance of the saints" is that those whom God has saved can never permanently fall away. Some implications flow from this idea, such as the view that a Christian can (but might not) have assurance of his or her own salvation. But the core of the doctrine is that God grants perseverance to those that he saves.
The church father that Calvin relied on the most was Augustine, and as expected, he is the most significant early proponent of a "perseverance of the saints" view similar (but not identical) to Calvin's. Here are a few quotes from his work, On the Gift of Perseverance:
I assert, therefore, that the perseverance by which we persevere in Christ even to the end is the gift of God; and I call that the end by which is finished that life wherein alone there is peril of falling (1)
When that gift of God is granted to them,—which is sufficiently plainly shown to be God’s gift, since it is asked of Him,—that gift of God, then, being granted to them that they may not be led into temptation, none of the saints fails to keep his perseverance in holiness even to the end. (9)
When, therefore, God’s hand is upon Him, that we depart not from God, assuredly God’s work reaches to us (for this is God’s hand); by which work of God we are caused to be abiding in Christ with God—not, as in Adam, departing from God. For “in Christ we have obtained a lot, being predestinated according to His purpose who worketh all things.” This, therefore, is God’s hand, not ours, that we depart not from God. (14)
Unlike Calvin and the Reformed tradition, however, Augustine didn't hold that a believer could have true assurance of salvation. The first quote above (chapter one) continues:
Therefore it is uncertain whether any one has received this gift so long as he is still alive. For if he fall before he dies, he is, of course, said not to have persevered; and most truly is it said. How, then, should he be said to have received or to have had perseverance who has not persevered? (1)
Reformed theologian Louis Berkhof summarizes Augustine's position as follows:
He held that the elect could not so fall away as to be finally lost, but at the same time considered it possible that some who were endowed with new life and true faith could fall from grace completely and at last suffer eternal damnation. (Systematic Theology, 4.11.A)
Perhaps a clearer way to say this is that of the many who receive blessings of faith and life, some are elect, and some are not. The elect have been given the additional gift of perseverance from God. This is opposed to Calvinism, in which the gifts of election, faith, life, and perseverance are all bound together.
Thus Calvinism diverges from Augustine in at least these two ways. But the basic principle, that a man's perseverance depends on God's gift, and not his own efforts, can be traced to Augustine.