It is the same as the system that grants you artifacts from slaying Paragon creatures, or slaying creatures in the Anti Virtue Dungeons. The points you receive are cumulated and not lost when you leave or log out. However, you don't get an artifact when you reached a certain number of points, but the chances of receiving a reward are higher the more points you have. (In theory, you could receive a reward after slaying your first Gauntlet creature, however this chance is very very low.)
Whenever you received a reward, the number of associated points is reset to zero.
That's my understanding of how the system works.