Suicide is a grave sin equivalent to murder (Exodus 20:13; 21:23), but it can be forgiven like any other sin. And Scripture says clearly that those redeemed by God have been forgiven for all their sins--past, present, and future (Colossians 2:13-14). Paul says in Romans 8:38-39 that nothing can separate us from the love of God in Christ Jesus.
So if a true Christian would commit suicide in a time of extreme weakness, he or she would be received into heaven (Jude 24). But we question the faith of those who take their lives or even consider it seriously--it may well be that they have never been truly saved.
That's because God's children are defined repeatedly in Scripture as those who have hope (Acts 24:15; Romans 5:2-5, 8:24; 2 Corinthians 1:10, etc.) and purpose in life (Luke 9:23-25; Romans 8:28; Colossians 1:29). And those who think of committing suicide do so because they have neither hope nor purpose in their lives.
Furthermore, one who repeatedly considers suicide is practicing sin in his heart (Proverbs 23:7), and 1 John 3:9 says that "no one who is born of God practices sin." And finally, suicide is often the ultimate evidence of a heart that rejects the lordship of Jesus Christ, because it is an act where the sinner is taking his life into his own hands completely rather than submitting to God's will for it. Surely many of those who have taken their lives will hear those horrifying words from the Lord Jesus at the judgment--"I never knew you; Depart from me, you who practice lawlessness" (Matthew 7:23).
So though it may be possible for a true believer to commit suicide, we believe that is an unusual occurrence. Someone considering suicide should be challenged above all to examine himself to see whether he is in the faith (2 Corinthians 13:5).