Your site is not loading the Bootstrap Javascript library. There is a setting in JFBConnect, defaulted to "On", for "Include jQuery / Bootstrap". It seems as though you've turned that off, but aren't loading that library on your own. (In v5.2.0 an v5.2.1, the seeing is called just "Include jQuery").
The "Show 'logging in' popup" setting in JFBConnect, which you've enabled, requires Bootstrap to show the modal popup during authentication. Because it's not there, you're getting a Javascript error and that's preventing the login process from resuming.
I hope that helps, but if not, let us know.
Thanks,
Alex