Could you try checking to see if there are any system or user plugins trying to redirect users after authentication? Some examples are the JomSocial redirect plugin or the redirection URL settings in the Community Builder system plugin. Also, if you're running any SEF extensions, please make sure to exclude JFBConnect URL's as it can interfere with the social networks calling back to the website.
Besides redirection settings/plugins, caching is another common cause of problems like this. Could you try disabling caching and temporarily disabling any cache plugins like the system cache plugin or jotcache, etc to see if this helps.
Try looking into redirection settings and caching first and let me know if this helps.
-Melissa
Can't get Auto Subscription working on JFBC keeps looping
