I'm not really sure what you mean by this. Are you saying that 'normal' Joomla users are able to edit their profile, but once they connect their account to Facebook, they no longer have the ability to edit it?
That's strange behavior that we've never heard of before. In general, JFBConnect creates 100% standard Joomla users and only 'extends' the user with additional information about their social network connections. My best guess in this case is to ensure that the users that are linked by JFBConnect to a social network are in the same User Group as all other users. You can view the user groups in the User Manager and possible in some section of your DJ Classifieds component.
I hope that helps narrow things down, but if you get any more information on what's going wrong, just let us know.
Thanks,
Alex