Why do the saints persevere? Because God finishes his work.
Think of it this way. There are only three things that could possibly cause a person to lose their salvation. These are the three categories to cover, God, the Devil, and man. Here are the scenarios:
(1) God forsakes them
(2) The Devil or some other wicked person tricks and steals them
(3) They ruin themselves or shrivel up
The bible teaches that none of the above will ever happen to a true Christian. John's gospel makes this clear.
(1) John 6:37 - the one who comes to Me I will certainly not cast out...
(2) John 10:28 - no one will snatch them out of My hand...
(3) John 15:16 - You did not choose me, but I chose you, and appointed you that you would go and bear fruit, and that your fruit would remain...
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With these three categories covered we can see a bit more clearly why Jesus said, "Of those the Father has given to me, I lose nothing." Praise God.