Your site is still loading a IP address in a frame. As mentioned above, I believe that's the main culprit and is what needs to be fixed. The other suggestions were ideas that may work around that issue, but if not, the solution is to load your content from a real domain.
I just tried to register, and I got an error "This email is already registered.". It's likely you don't have the Automatically Connect Users by Email address enabled and I already have an account on the site for some reason. In any case, it seems like it did work for me as it's getting my email from my profile. I didn't see the access token error you mention.
I still think using a real domain may help. If not, please test with different users on different computers and let me know if it happens for all Facebook users, or just some. Also, please delete my account on your site or enable the setting I mentioned above and I can test more.
Thanks,
Alex