I can see what you're talking about. I just registered, then went back to the home page and clicked the Signup/Login button again. On the login page, it showed me as logged into Joomla but JFBConnect was not detecting that I had logged in through Facebook.
This is uncommon, but there are some things to check:
* Please try disabling any User plugins other than Joomla, JFBConnect, and JomSocial. Some User plugins have been known to conflict with JFBConnect
* Please disable any Authentication plugins other than Joomla, JFBConnect, and JomSocial.
* Try re-ordering the JFBCSystem plugin to the highest (lowest number) position and then the lowest (highest number) position, but before any optimization or caching plugins
After each test above, please clear your Joomla cache and restart your browser to make sure the new settings take effect. If one of those helps, let us know which it is and we'll help you re-enable any functionality that may have been disabled or changed.
If none of that helps, I'd have to ask you to Private Message me a set of super admin credentials so we can investigate further.
Thanks,
Alex