How are you restricting access to that section of your site? JFBConnect will set users to the 'default' user group configured in Joomla. If you're using the permissions in Joomla to restrict certain areas to certain groups/access levels of users, that could be the problem.
If not, please check that the Redirect on Login or Redirect on Registration settings are going to the proper URL.. one that is visible to normal registered users. If that doesn't help, then can you try registering through the normal Joomla process and see if you run into the same issues when logging in that way? If not, check what user group both the Joomla and Facebook user are in and see if they are different.
Hope that gets you started,
Alex