The Gospels:
In John 8:31-32, Jesus is talking to the Jews who have professed belief in him. In the context, what we see is that these Jews ultimately show that genuine faith is lacking. Jesus tells them "If you continue in my word, you are my disciples, and you will know the truth, and the truth will make you free."
Jesus is telling the Jews who have professed belief in him that true faith will show itself in a continual abiding of Christ's teachings. Those who, like these Jews, turn and walk away after a hard teaching show that their faith was never real in the first place.
In Matthew 10:16-25, Jesus is telling his apostles all that they will have to suffer for the sake of the gospel. After mentioning all the persecutions and sufferings they will face, he then states in vs 22 that "...the one who endure to the end will be saved." What Jesus seems to be teaching here is that genuine faith will prove itself genuine by enduring all the way to the end. In spite of the persecution, in spite of the pain, the loss, and the heartache, the true believer will never throw in the towel and walk away from the faith during times of persecution. Thus, he will be saved.
Paul:
In his letter to the Colossians, at the end of the first chapter, Paul is speaking to them about their reconciliation. He says that God has done this, "in order to present you holy and blameless, irreproachable before him, provided that you continue in the faith, stable and steadfast, not shifting from the hope of the gospel which you heard" (1:22-23).
Why would the apostle who holds so strongly to the doctrine of election say such a thing? It must be taken into consideration that Paul obviously does not know the heart of every single individual that he is writing to who professes Christ. There have always been false converts, and it wasn't any different in Paul's day. How is he supposed to distinguish between the true and the false? How is he supposed to write to these people and not give false converts a false hope? He speaks this way because he knows that only those whose faith is is real will continue in it.
Rest of the New Testament:
Hebrews 3:14 emphasizes something similar to Col. 1:22-23. In 3:14, the author states, "For we have come to share in Christ if indeed we hold our original confidence firm to the end." The author will pick this theme up many more times throughout the book. He is writing to Jewish Christians who are contemplating walking away from the faith during a time of trial and persecution.
How do they know they have become partakers of Christ? How do they know that they have been joined with Him? According to this verse, they know because they endure. Continuing in the faith is thus one means of assurance that God uses to affirm to His people that He will not let them go.
Finally, it must be reiterated that faith is a gift that God gives His elect, that comes to them through the preaching of the gospel (Eph. 2:8-9; Rm. 10:17). What this means in regards to the perseverance of the saints is that though faith is required for perseverance, the very thing required is a freely given gift. God does not leave His elect to their own resources. There was no way that they could make themselves believe apart from grace, and there is no way they can make themselves persevere apart from grace. Again, let me state it this way, the very thing that God requires for perseverance is the very thing He freely gives- faith. Why will the true believers endure to the end? Why will he persevere? Because not only is he safe in the grip of God, but he is also empowered by the gift of God.
In the next post, we will look at a number of passages that some have used to support the teaching that genuine believers can indeed fall away from the faith. After we deal with these passages, we will wrap up this segment with some practical applications of the doctrine.