"Until he dies" is irrelevant.
"Incorporated into Christ by Baptism, the person baptized is configured to Christ. Baptism seals the Christian with the indelible spiritual mark (character) of his belonging to Christ. No sin can erase this mark, even if sin prevents Baptism from bearing the fruits of salvation. Given once for all, Baptism cannot be repeated."Death does not remove the mark from the soul.
- Catechism of the Catholic Church, 1272
RE: Death does not remove the mark from the soul.
So, how does Baptism save the soul of the unrepentant unbeliever?