This is an age-old Christian debate and the confusion is based on looking at one side of the problem to the exclusion of the other. However, before we begin, let us remind ourselves of a couple of simple NT teachings:

1. Salvation is the Initiative of God alone
2. God wants all people to be saved by grace
3. God's gracious Will
4. Many reject God's will and offer of Salvation
5. Christian Distractions from perseverance

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Summary/Conclusion

We are saved by grace alone, through Christ alone, by faith alone and this is the initiative of God alone by the miraculous work of the Holy Spirit. However some refuse to accept this and reject the faith granted to them (Rom 1:18-23) and so become lost. It is by continuing to believe and trust in God and the divine strength He imparts that a Christian perseveres.