Eventually, yes. I think even Seachem says so. The more you regenerate, the more quickly you'll need to regenerate again. In my mind, it's basically the (vastly) superior version of charcoal. As long as it's in a media bag, you'll be fine. You don't even need to use The Bag, because that thing is designed to withstand any of the regeneration processes for any of Seachem's media, some of which utilize muriatic acid instead of bleach, for example. Bleach is much less caustic, and I've got some Purigen in a media bag I got from PetSmart for like a dollar that's already been through a regeneration, and will probably go through another in the not too distant future.
However, your initial question seemed to be about exclusively using Purigen. Why would you do something like that? It's chemical filtration. Why would you remove your mechanical and biological filtration? I know the words sound like I'm berating you, but that's not my intention. I'm confused as to why you would think to remove the other filtration types, since typically, chemical filtration is the optional one of the bunch.