Caveat: "My thoughts are not your thoughts and My ways are not your ways, says the LORD" (Isaiah 55)
After that caveat: Suicide is a violation of the commandment to do no murder. So it is a sin.
The question which we dare not answer (lest we be guilty of the primordial sin of wanting to be like God) is whether it is an unforgiveable sin.
Is God's forgiveness dependant upon our ability to ask for forgiveness...our ability to repent? Some would say that a sudden gunshot to the head allows for no possibility of repentance and therefore is unforgiveable.
Others point to the promise of the Psalms that "the LORD is near to the brokenhearted and those who are crushed in spirit He saves."
Ultimately, it is neither for us to know or to judge. Back to Isaiah 55.
Yet people will judge, like it or not.