"If any man see his brother sin a sin which is not unto death, he shall ask, and He shall give him life for them that sin not unto death. There is a sin unto death: I do not say that he shall pray for it" (I John 5:16).
The "sin unto death" is, in context, a sin committed by a Christian "brother," not an unbeliever, and so is not the so-called "unforgivable sin," the blasphemy against the Holy Spirit. Christ said the latter sin cannot be forgiven, "neither in this world, neither in the world to come" (Matthew 12:32). It is the ministry of the Holy Spirit to convict unbelievers "Of sin, because they believe not on me" (John 16:9). If a person irrevocably rejects Christ, even after he fully understands the evidences of His deity, His substitutionary death with its offer of salvation, and the awful consequences of eternity without Him, then he "hath done despite to the Spirit of grace" (Hebrews 10:29). In effect, he has put his faith in Satan rather than Christ, and there is nothing more that God's Holy Spirit can--or will--do. This is the truly unforgivable sin.
The Christian can persist in some known sin, though not the sin of total unbelief or willful apostasy (a true Christian will not commit that kind of sin). If he deliberately continues to practice ungodliness in life or doctrine, however, refusing to repent, not even responding to God's chastening discipline (note Hebrews 12:5-11), then the only recourse of the Lord may be to send physical death, although not eternal spiritual death, for such a person is delivered "unto Satan for the destruction of the flesh, that the spirit may be saved in the day of the Lord Jesus" (I Corinthians 5:5).
This is a fearful prospect even for the believer, and should be a sober warning against persistence in any known sin. "He shall suffer loss: but he himself shall be saved; yet so as by fire" (I Corinthians 3:15). HMM