The JFBCLogin module has a parameter to enable whether to show the Login button after the user's already logged in. Other than that, there's not really a permission for it.. if you make some modifications to the { JFBCLogin} tag, which shows the Login With Facebook button, to have it show when a user is logged in, it will reconnect the user as well.
Hope this helps, but if you explain more of what you're trying to do, we can help you more. Are you trying to allow reconnections, using the module or the tag, etc?
Thanks!
Reconnect Button
