Whenever I answer a question about suicide, I'm always aware that someone who's thinking about ending their life might be reading it, and would misunderstand my answer. Let me be clear: Suicide is never God's will, and the Bible's command telling us not to commit murder includes not murdering ourselves (see Exodus 20:13).
Nevertheless, God knew your uncle's mental distress and confusion -- and no, suicide is not the unforgivable sin that Jesus mentioned. Suicide is serious (as I have said) -- and it's especially so when the person has never faced his or her need for God, and turned to Jesus Christ for forgiveness. But God alone knows their heart, and He alone -- not us -- is their judge.
What is the unforgivable sin? Jesus defined it this way: "Every sin and blasphemy will be forgiven men, but the blasphemy against the Spirit will not be forgiven" (Matthew 12:31). We blaspheme against the Holy Spirit when we declare that His witness to Jesus Christ is false, and we reject it. It is the sin of denying the Holy Spirit's witness to Jesus Christ as our Savior and Lord.
Ask God to make you more sensitive to those around you who may be going through hard times, and may even be wondering if life is worth living. Then ask Him to help you point them to Jesus Christ, who loves them and can give them hope -- for today, and for all eternity.