First, the easy stuff:
1) Make sure the JFBC authentication and user plugins are enabled
2) If you have any other Facebook related extensions, temporarily disable them and test.
3) If you're using an SEF extension, try disabling it temporarily, and see if that fixes the problem (if so, we can help you re-enable it)
4) Try turning on "Automatically Login Facebook Users" and see if that logs you in
5) Enable a different template and try to login.
I just tried on your site, and I am seeing the same issue. Not sure what's causing it though. Hopefully, the above helps make progress. If not, let us know, and we'll help out however we can.
Thanks,
Alex