Suicide is murder. After all the person is killing one of Gods children. I do think though that if a person has an unbalanced mind, or some kind of chemical unbalance God would judge with that in mind.
People, believers, often like to make caveats on how God will judge a person but the problem with this is that these special case scenarios are irrelevant in that Jesus already paid the price for sin. If suicide is a sin, did not Christ pay the penalty of all sin on the cross?
Of course this isn't an endorsement to commit suicide, but if you look at the Gospel and what Jesus accomplished through His death and resurrection you cannot argue that suicide leads to eternal damnation if suicide is a sin. Why? Because, Jesus is the propitiation for the sins of the world, He is the appeasement to God's righteous judgement. His blood is sufficient.
One must keep in mind that if a, truly, born-again Christian commits suicide God already knew that was coming and chose to save them. Just like every one of us, God already knows the sins we will be committing and yet He gave us new life. He took us who were dead in our sins and gave us life in Christ unto good works.
You see, thats the sad thing about suicide. Those good works never come to be that could've possibly been. How many people could've they encountered and the Holy Spirit convict, to bring to Christ? So many possibilities lost. Suicide as awful as it is does not supersede Christ's finished work on the cross. Its awful, its sad, but its not damnable. Jesus reigns supreme, He loses none that are His.
PS: A person contemplating suicide is in dire need of hope and purpose. These God offers, just simply seek His will for your life. If you are in Christ, if you are a believer, then you have a purpose within the body of Christ as one of its many members. Each part being essential to its respective role, you are invaluable. Jesus died for you. Take that to heart, and instead of taking your life maybe you'll rather give it to Jesus.