He fell in love with a married woman and devised a plan to have her husband killed in battle, so he could have her. But when Nathan, the prophet, confronted him with the deed, David repented in sackcloth and ashes. Restore unto me the joy of thy salvation. Those are the words of a man who knew beyond a doubt he was bound for heaven. Even though suicide is not an unforgivable sin, it grieves the heart of God and leaves a scar on the family that never goes away.
Life is too precious to be terminated by ones own hand.
That's A Good Question by R.C. Sproul, and Tough Talk About Tough Issues by Bob Larson.