Dr. Nicole writes:

The last point [in TULIP] is called “the perseverance of the saints,” and the emphasis is that those who have been won by the grace of God will not lose out but will be preserved by God’s grace to ultimate salvation. It means that it is not possible for one who is truly regenerate to fall out of the reach of divine grace, lose salvation altogether, and finally be lost.

The advantage of this formulation is that there is, indeed, a human activity in this process. The saints are active. They are not passive. In a true sense they are called upon to persevere. But there is a devastating weakness in this formulation in that it suggests that they persevere because they are strong, that they are finally saved because they show that kind of stability and consistency which prevents them from turning back into their original wickedness. This is never the case. The key to perseverance is the preservation by God of his saints, that is, the stability of his purpose and the fixity of his design. What is to be in view here is not so much the perseverance of those who are saved but the perseverance of God with the sinners whom he has gloriously transformed and whom he assists to the end. We ought to talk about “God’s perseverance with the saints.” That is the proper emphasis.

Our Sovereign God is a wonderful book on the doctrines of grace. More information about this resource can be found here.

Some proof text for  “God’s perseverance with the saints.” — This list is not Exhaustive

1. John 6:38-40
2. John 10:27-29
3. Ephesians 1:13-14
4. Philippians 1:6