Hmmm. That's a strange one that we haven't heard of. How did you remove JFBConnect, the normal Uninstall method within Joomla? When you re-installed, did you see any errors that you recall? Finally, can you try going to:
/administrator/index.php?option=com_jfbconnect
And see if the page loads correctly? That will help us know if it's just the menus that are missing, or if there's more problems underneath.
Thanks,
Alex