It is a tricky situation. It came up several times for my swordmage, since they don't have to worry about maintaining a mark.
The problem is, the rules don't say it goes away aside from when it would normally expire. But it both seems strange to have it persist when the character isn't there to be applying it, and it is potentially dangerous since it would encourage enemies to attack dying PCs.
I think the way we ran it in my group is that the mark remained until it would normally expire, but did not actually function as long as the character was dying. So if they got healed up in time, they wouldn't need to reapply it (aside from when they would normally need to do so), but it wouldn't cause issues while they were dying.