Please try the following:
* Disable caching on your site. Specifically in the Joomla -> Global Configuration area, but possibly anywhere else that you have have 'optimization' plugins enabled
* It looks like you're using a 3rd party SEF extension. Please make sure that whatever extension it is is set to "Skip" altering JFBConnect URLs
Then, test again. If that doesn't work, please try disabling SEF URLs altogether to see if that helps the looping issue.
If that fixes things, we can help to re-enable caching or any other changes you made, but we need to narrow down where the conflict is first.
Thanks,
Alex