I have to agree with bubbaganoosh's reply. The Holy Spirit will not leave during the rapture but His ministry will change. The believers of that day will not have Him sealed in them as we in the church age have Him sealed in us. But those people will still have to trust in Christ's atonement for their sin and never take the mark of Antichrist even to the point of death.
Mark 13:31 Heaven and earth will pass away, but my words will never pass away.
Coming again coming again maybe morning maybe noon maybe evening and maybe soon!
Coming again coming again O what a wonderful day it will be! Jesus is coming again!