I just registered an account on your site. After logging in, there was a Logout button in the top right corner. That doesn't look to be coming from our SCLogin module. I'm not sure why it's not working as it looks correct, but I'd recommend trying our SCLogin module to see if the logout button in it works.
Additionally, please try logging in with a standard Joomla user account (not a social network) to see if that has the same issue. If it happens for all users, then it's not related to JFBConnect at all. I'm not sure what it would be, but it indicates there may be an issue with your Jooml installation.
I hope that helps narrow things down and get things going for you.
Thanks,
Alex