Yeah, I'd really recommend looking into removing that. The 'main' domain that the frames are loaded from are then loading the other frame from a different domain. Each Facebook Application has an "Application Domain" setting. In your case, I'm assuming it would be the 'framed' domain that you should use, but no matter what, it's a bit confusing and I don't know how Facebook truly 'sees' your site. It definitely could think things are suspicious and mark your app as spammy or something like that, which requires more steps from users to login, Like, or otherwise interact with the site.
So, hopefully, the above helps get you going, but I'd really look at the frame stuff. Again, I can get to the Login / Register page. If you're seeing the loop after the user has registered, let me know, and I can register and then try to login and test some more. Right now though, I can't see any issues directly... but I can see how problems may be happening with the framing situation you're in.
Hope that helps,
Alex