I saw this question posed tonight and thought I'd answer with my thoughts - so here's what I said...
I have wondered this very thing and here is the best I can tell you on the matter....
I believe that once a person accepts Jesus Christ as his/her personal savior they are going to heaven when they die (or when Christ returns - whichever comes first ;o). I believe that NOTHING can separate us from the love of God once we've accepted His son. ( Romans 8:38-40 ).
Now, why do people commit suicide? Obviously the reason they think they are doing it varies from person to person - but what is the one common underlying theme in most instances? Wouldn't you say it is an absence of "hope". They feel "hopeless" about something(s) and so they opt out. To know Christ is to know "hope", it's to have "hope". So, I guess we could assume that to commit such a "hopeless" act might indicate that the individual wasn't really a Christ follower in the first place?
Obviously none of us can say with absolute certainty one way or the other. Only God can truly answer that question. He knows the hearts of those who resort to such a thing. I have heard some denominations say that the individual would most definitely go to hell because to murder is a sin (true) and having done this they sin and are unable to ask forgiveness before death. Well, suppose I stubbed my toe and swore (sin, taking the Lord's name in vain) and then while walking to my car I was hit by a bus and killed. Would I go to hell because I hadn't begged God's forgiveness before I died? I don't believe so. If this is so, then why did Christ die on the cross? If we are Christ followers and have accepted His free-gift sacrifice for our sins - then isn't His blood sufficient to cover our sins? This doesn't mean we are to go on sinning without any consequence or remorse. No, we're to follow Christ's example for sure, but it is impossible for us to be perfect - hence why God sent Christ in the first place. So to say that somehow our salvation can be taken from us really makes Christ dying on the cross for our sins pointless doesn't it?
I believe the only "unpardonable sin" is the sin of rejecting Christ. I'm not sure if I've answered your question but thank you for making me think a lot tonight ;o)