I just went to your site and was able to successfully create an account with my Facebook test account (Melissa Lynne SourceCoast). When I logged out I was able to successfully log back in with no issues. Are you still experiencing this problem? Have you tried logging into your site with a different Facebook user - is it reproducible with a different user?
If so,
* Can you re-run the error check in JFBConnect backend > Autotune? Are there any obvious errors / missing field entries in the Autotune > FB Application tab?
* Can you verify that the FB account that you're trying to log in with has an entry in the JFBConnect > User Map area? If not, can you see if there are any existent Joomla users with the email address?
* Can you try disabling the loginfailedlog plugin to see if there's any improvement? The majority of the warnings in that screenshot are not from us.
* What version of JFBConnect did you upgrade from?
-Melissa