If the Swords negated Nic's healing factor, I'm relatively certain that he would've been killed by a Knight at some point over the last two millennia.
To the OP: It's something that nagged at me, too, and I don't have an answer for it. The only thing I can come up with is that the fight took place over a much shorter time than you'd think from the way it was written, really only taking a few minutes (albeit over several dozen pages), and that Nic did indeed heal back up once he fled.