JFBConnect doesn't have any interaction with the normal Joomla login process. We use the Joomla authentication system to perform authentication. Our SCLogin module is a front to that functionality.
With that said, what I'd recommend is testing with the standard Joomla login module (mod_login) to see if that functions properly. If it does, one thing you can try is setting the "Cache" setting in the SCLogin module to 'disabled'.
Hopefully that works, but if not, try disabling any other caching options you may have enabled on your site and test with both login modules again to see if you have better results.
Thanks,
Alex