Forgiveness of suicide, as with all sins, is contingent on one's relationship to Christ. If you are apart from Christ, you will not be forgiven whether you commit suicide or not. (see Colossians 1:14 and John 3:16-18)

More specifically, I believe you're asking if a Christian can commit suicide and still be forgiven and go to Heaven. That question too has its answer in the finished work of Christ. Hebrews 7:25 tells us, "Now He is able to save completely all those who come to God through Him, for He always lives to intercede for them." According to this verse and its immediate context, the forgiveness of sins by God to all who believe and receive Jesus Christ, is based in the continuity of Christ's ministry and the perfection of His self-sacrifice, once for all.

Notice it is absolutely not contingent on our ability to continually ask his forgiveness for our sins. If we know Christ, we are justified by God once and for all time, as the Greek tense of the verb for "justified" in Romans 8:30 indicates God's one-time act with consequences going forward forever.

No, this is not a license to sin, as the Spirit said through the Apostle Paul, "May we continue sinning that grace may abound? May it never be! How shall we who died to sin continue to live in it?" (Romans 6:1-2)

Many other passages speak to the eternal security of those believers who endure to the end. (see Philippians 4:13, Romans 8:29-31, Revelation 2:26-28) Even the so-called "problem passages" in the book of Hebrews, are seen most clearly in the context of God disciplining His sons--an encouraging not a dreadful thing. (see Heb. 12:5-12)

The question with suicide is one of whether or not the person truly endured to the end. If the suicide was a moment, albeit a big one, of temporary weakness, then that believer would be ushered into the saving presence of God in Christ Jesus. If the suicide was but a mere symptom of the person's faith getting "choked off by the cares of the world," then certain judgment by Christ Jesus Himself awaits the suicidal one.

In all this, only God knows the true condition of a person's heart at death--suicide or not. If you're found in Christ Jesus through believing in Him as evidenced by your enduring in His strength to the end, then you already stand saved by His perfect, eternal High Priestly ministry--chiefly through His offer of Himself once for all for our sins. (Heb. 7:27; I John 5:11-12)

I pray this helps...