Invisibility purge is like a very specialized antimagic; any effects that cause invisibility are suppressed while in the area. There's usually no way to resist.
A very few creatures have special, innate invisibility that is unaffected by the purge. And of course, it doesn't help against creatures who are disguised or just hiding. If you really need something to get into that area unseen, send an Invisible Stalker, or a disguised changeling, or somebody with an insanely high Hide check.