I believe in the doctrine of the preservation of Christians, but not in automatic perseverance. The Christian life isn't lived on auto-pilot, where we can kick back and go to sleep while the plane just flies on.
God preserves His people in His redeeming love. There is no created thing that can separate us from the love of God in Christ (Romans 8). A Christian is part of the creation, too, so not even we can separate ourselves from God's saving love. God's gifts and calling to us through Christ are irrevocable.
However, the New Testament is filled with warnings about how a Christian's faith can shipwreck. Check out the two epistles to Timothy, and the book of Hebrews, and see how many warnings there are about what can go wrong with a Christian's faith. God does not warn in vain.
God never exhorts Christians to beware sins that we are constitutionally incapable of committing. The new birth does not make us perfectly loyal to Christ. Peter denied he knew Christ. The Corinthians doubted the bodily resurrection. The Galatians were adding works to grace. Ananias and Sapphira lied to the Holy Spirit. Demas loved the world and abandoned Paul in his distress. These were all saved people.
When God warns Christians to stay faithful to Christ, the act of giving the warning in itself proves it is possible to be unfaithful to Christ. God doesn't warn us against sins we could never commit, any more than He warns us against blue unicorns or snow falling up.