Hannah's started doing that in the last week or so.
Luckily, she has no teeth, but her gums are damn hard!
Nothing I seem to do stops her from doing it.
DH thinks it's her way of telling me she's had enough, so I let her play (*eta: with her toys, not with me

) for 10 minutes and try again. If she's still biting, then I just assume she's no longer hungry.
Sorry - I'm not much help. Just wanted to let you know the same thing's happening here and I'll watch this thread for advice, too.
Edited by MamaPickle