I would have serious doubts about the genuineness of faith of anyone who claimed to be a Christian yet committed suicide.
That's a very interesting perspective on suicide and salvation, one in which I've never heard used in this debate, and thinking about it, I would have to agree completely. There's the usual arguments about suicide being "unforgivable" because it's murder, or because the final act denies one the chance to repent, taking one's life against the will of God, etc. But suicide as the outward action and expression of one's relationship to God makes perfect sense.
I believe that once a person is saved, nothing can tear us apart from God and cause us to lose our salvation, unless the person turns away and rejects God himself. But anyone coming to God and saved by Jesus Christ is imbued with the Holy Spirit and with that comes hope. No matter what circumstances fall upon us, no matter what personal struggles we endure, Christ in us means we put our faith and trust in God. We have hope because we believe in what his word says about him, what our personal experiences with God reminds us, and all of God's promises for the future.
But the act of killing oneself to escape one's suffering and this world is the final resolute act of desolation, desperation, and loss of all hope. One would hold off suicide if there is even a glimmer of hope that things can get better or that life is worth living. But suicide means the complete absence of all hope. For the Christian, that would mean you have lost all faith and trust in God, his sovereign ability to be in control of all things, and his willingness to help you through the worse of times and see you prosper in life.
Suicide is always a tragic event. But when seen from this perspective of what it must mean for someone who had tasted the joy of faith and trust in God to then find himself feeling completely abandoned and rejected that he no longer has hope, that even God can't help them, is so utterly sad to me. So much so that it's perhaps even unbelievable, for the Bible says that anyone who has tasted the goodness of the Lord can never turn back. This would lead to the conclusion that perhaps the person committing suicide have never really experienced the joy and hope of placing their life in Christ.
Having said that, I understand that life happens and some things can get us really depressed and feeling hopeless. For me, during those hard times it's hard for me to think about anything else, so it's been really helpful to remind myself that God is still there. Remembering how he's been there in the past and that he's unwavering, reading his word and promises, and even having supportive friends and family all help to refocus attention and remind that yes, hope lives.