First, double-check that you're using the latest version of JFBConnect, currently v8.0.6. There have been updates in both 8.0.4 and 8.0.5 to make some updates for the upcoming shutdown of Google+ and to ensure compatibility with Google's new single-sign on system.
Beyond that, if you're still having issues, we recommend:
* Temporarily disabling all caching on your site
* Temporarily disabling all 'optimization' features on your site. Things that compress or rejig your Javascript could cause a problem (but unlikely if Facebook is working)
* Temporarily disable SEF URLs on your site
Once those are disabled, try again and see if things work. If so, re-enable one by one to see when things break.
If it still fails, sometimes when the user is returned to your site, the URL in the address bar will have a long string in it that has a decent explanation of what's wrong, like "User+hasn't+granted+permission". If you can't find it, or just need our help, let us know what URL we can test on and we'll gladly help investigate further.
Thanks,
Alex