It has been traditionally taught that suicide is a mortal sin. There are a list of sins that the Church developed, apart from Scripture, for which they declared that there is no forgiveness. However, Scripture only teaches that there is one sin that God will not forgive, and that is blasphemy against the Holy Spirit. You can read more about that here.
When we understand reality and life, we realize that a worldly life is meaningless. Whatever we gain here on the Earth of physical pleasure cannot be taken on to the next life. Treasures that our cultures and societies value are destroyable by moth and rust (Matt 6.19). Life is vanity (Ecc 2.1). Worldly pleasures are vanity. They cannot satisfy.
But Jesus offers us hope and an eternity. He died on the cross and took my punishment and yours so that we can have eternal life. Life in the fullest. And that life starts now (John 3.36) He gives eternal meaning and purpose.
So can a person who knows and trusts in Jesus lose hope to the point of taking his own life? Jesus says that nothing can separate us from the love of God (Rom 8.38). He says that nothing can pluck us out of His hand (John 10.28). John says that when we sin, we have an advocate before God -Jesus Christ – who lives to make intercession for us (1 John 2.1; Heb 7.25). That means He stands there and the accuser (Satan) points out our sin, and He says, “Yes, he did that, but it has been paid for”.
The reality is that whenever anyone who loves God sins, he lapses in hope, faith or trust for a moment. Whenever we choose the things of the world, we choose enmity with God (James 4.4).
But suicide is unique in that there is no opportunity to confess or repent, and that is why the church deemed it a mortal sin. scripture does not teach that, and it us always dangerous to speak where God does not. What we do know is that Jesus died to redeem us. He paid the penalty for our sin. When we repent from our sins and trust Him for life and salvation, we are saved and made justified before Him. We all sin after coming to faith, and Jesys tells us that only blasphemy against the Spirit will not be forgiven.
Therefore I would argue that suicide, though a terrible sin and a deeply profound exemplification of a lack of faith and hope, is not unforgivable. A person who knows and loves God can get distracted and discouraged by the world. Not all who commit suicide are forgiven, as not all have sought repentance in their lives. But Christians can suffer from physiological imbalances, depression and the burdens of life.
God of promises us that all things work together for good for those who know and love Him ( Rom 8:28). To kill one’s self is to not believe this promise, at least in the moment. We should seek to trust Him in this promise and not embrace suicide as an option. It is sin. But we should not surrender hope for those loved ones in our lives who have succumbed to the temptation and taken their own lives. God’s grace is bigger than suicide.