We did not see Jesus praying for Sinners. He responded with Forgiveness and Healing to those who Believed on Him after Hearing Him Preach and Teach the Gospel of the Kingdom.
God does not violate the FreeWill that He has given to each of us. To Pray that God Save someone who has rejected the Gospel is to ask God to Deny Himself.
In this passage Jesus Prays by Faith for those who WILL Believe. He did not name names. Neither should we.
The HolySpirit reacts to a person's response to the WordOfGod which we share to Deliver, to Heal, to Save or to Condemn. Yes, the HolySpirit Condemns a person who rejects the Gospel of Jesus Christ. He does so by no longer drawing them to the Truth which they have willfully and knowingly rejected.
The UnpardonableSin is a lot easier to commit than people think. Jesus instructed His Disciples to shake the dust off their feet as a Testimony AGAINST those who rejected the Gospel of the Kingdom. Mat 10:14
But we are to Pray one for another aren't we? Yes, but this is talking about the community of Believers - the Body of Christ.
What about Praying without ceasing? This is in terms of Fellowshipping with God in the HolySpirit.