It is possible for someone who commits suicide to go to heaven. Even if one considers suicide murder, there are plenty of well-known murderers in heaven. It's not a question of sin or repentance, but whether or not their sins are forgiven.
The reason I think most people believe most who have committed suicide are not in heaven is because when someone commits suicide they have no hope. And hope is one of the stalwarts of a relationship with Christ. Another reason is that even biblical figures who were severely depressed didn't take their own lives, but asked God to do so. A couple notable examples are Elijah and Jonah. Even Job, though encouraged by his wife, would not curse God and die.
It's a question that hits very close to home because, without going into details, I had a brush with suicide many years ago -- enough to land me in the hospital.
The medical staff told my parents that my condition was "borderline." But here I am today.
I consider myself a lifelong Christian -- but many have told me I'm not a real Christian because of that event. Some co-workers and friends refused to speak to me again.
I have often asked pastors and other Christians if I wouldn't have made it, where would I have gone? No one can answer me with a straight "here" or "there."
I have asked God many times where I would have gone, but it seems to be one of those many, many things that I won't know the answer to until I see Him in heaven -- if it's an answer He would ever give, because I realize in heaven, it would not matter.