Once you have known people long enough, and have studied the nature and character of man, you come to see that the sin unto death is that of total, final rejection of God, in the face of all the truth. The person knows the total truth about God, has been convicted by the Holy Spirit that he/she is a sinner in need of a Savior, but he/she has totally, willfully rejected the Holy Spirit's call to repentance.
God does not force people to repent and follow Him. When a person has again and again rejected the Holy Spirit's conviction, his/her heart becomes ever the more hardened in sin, and so the sin unto death is the same as the unforgivable sin that Jesus mentioned, the sin of total, willful rejection of Christ in the face of full knowledge of the truth. Such as person, do not pray for, because God will not reveal Himself to someone who does not want Him. So this verse is the equivalent of Jesus saying, "If they do not hear you, shake the dust off your feet, and move on to the next city." Do not continue to badger someone who does not want Jesus, because if you do, then you will represent God as a forceful God who will not let people have the freedom to choose God or Satan.
So praying for this kind of person is futile, because nothing will change them, because God has given that person the freedom to either choose or reject Him, and He will leave them alone if they do not want Him. Yes, God can change them, for nothing is impossible with God, but He would be a God of force if he changes someone who does not wish to be changed.
Hope this helps. God bless you.