Wow, never heard of that. Our logout functionality simply calls Joomla's standard logout calls. The only reason we have our own logout call is simply to (possibly) call a Javascript function to log the user out of Javascript as well. The call for Javascript obviously isn't the issue.
If you want to take a look at the logout code, it's in /components/com_jfbconnect/controller.php at the bottom. There's a logout function. The top figures out where to redirect the user (pretty basic, though 20 or so lines because there's multiple configuration ways to redirect them), a simple SQL query to the database, and then calling Joomla's logout.. which could trigger a ton of other things, but nothing that should be specific to JFBConnect.
All I can think to recommend is trying with sh404 off completely (redirects can be annoying) and all user plugins disabled (except Joomla). Might help you narrow things down, but really clueless on this one, sorry to say.
Let us know if you figure anything out,
Alex