Never heard of that. Are you saying, when you're in the Module Manager of Joomla, you can't click on the red icon to publish it? Alternatively, if you click into the module, you can change the status there from unpublished to published. One of these should work, if not, are you getting any Joomla message explaining why it won't publish?
There's nothing in JFBConnect's configuration that would prevent the module from publishing, so it seems like a Joomla problem itself. Have you tried publishing any of the other extensions that come with JFBConnect, like the JFBCSystem plugin, JFBCComments module, etc?
If you have any more details, just let us know.