We do not always know whether a Christian's sin is unto death; for that reason my own suggestion is that we should be sure to pray for such a person if we are in doubt.
If we see that God is not going to answer, it could be that the person prayed for has committed a sin unto death. But I will continue to pray for such a person until the Spirit in some way makes it plain just what has happened in his life.
I believe that the sin unto death is a deliberate sin of a believer against better knowledge. When John wrote about committing this sin, he used the tense so often employed throughout his first epistle, the tense that signifies continuation of action.
In my opinion the sin unto death is a deliberately planned and willful persistence in some evil course with the guilty person presuming on God's grace or mercy.
The death that results from this sin, as far as I can determine from Scripture, is physical death, not spiritual death. There is a vast difference between the two.
There may be those who have said, "Since I am eternally saved, I can live just as I please." They willfully and deliberately ignore the new life within them and its urging to godly living. I believe such a person stands in danger of committing the sin unto death.
"Keep back thy servant also from presumptuous sins; let them not have dominion over me" (Ps. 19:13).