Thanks for your question.
Is suicide sinful? Is it the "unpardonable sin?" The "unpardonable sin" in the New Testament is to deny the work of the Holy Spirit when confronted with its clear and obvious working. So the authorities in Jesus' day committed the unpardonable sin when Lazarus was raised from the dead and because of that they plotted to kill Jesus. In cases where suicide is not the result of mental illness or other mitigating circumstance it is unforgiveable because, once committed, there is an end of life and of the ability to seek forgiveness. Can one be forgiven for attempted suicide? Certainly! Why? Because the sinner is still alive to seek forgiveness.
Is suicide sinful? Suicide is self-murder and it is most definitely sinful. By committing suicide, a person is saying, "My problems are too big for God to help me solve." This is a lack of faith. Whatever denies faith is sin. See Romans 14:23 "...for whatever is not from faith is sin."
No problem is bigger than God. Hear what the apostle John says in 1 John 5:4 "For everyone who has been born of God overcomes the world. And this is the victory that has overcome the world––our faith." This is what Paul says in Philippians 4:13 "I can do all things through Christ who strengthens me." If we have faith, we can overcome every obstacle in our path; defeat any temptation; achieve any goal.
To commit suicide is to say that this is not true. That God is smaller than our problems and that He doesn't care enough to help us in time of need. Salvation is impossible for one with such an attitude. However, if we will take the time to build a real faith - one that is built solidly on His truth as revealed in His word, then, as Paul says in Romans 8:37, we will be more than conquerors in Christ. Romans 8:37-39 "Yet in all these things we are more than conquerors through Him who loved us. For I am persuaded that neither death nor life, nor angels nor principalities nor powers, nor things present nor things to come, nor height nor depth, nor any other created thing, shall be able to separate us from the love of God which is in Christ Jesus our Lord."
There may be some exceptions to the rule that suicide is sin. Some people are beset by a medical/mental condition which leads them to take their own lives. They may not be responsible for their actions. We know that God judges righteously and will not punish a person for doing something over which he or she has no control. Such a person would do well to take advantage of the wonderful advances in medical and psychological science available to us today to help in dealing with such conditions. These advances are blessings from God and we would be foolish not to make use of them when the situation calls for such intervention.
I hope you have found this helpful.
God bless and keep you,