Jeroen,
Your correct, the Remember Me checkbox does not work for Facebook logins. It can't for multiple technical reasons.
In Joomla, there's a session timer set in the Global Configuration area. If there is no activity for the user within that session timeout, they will be logged out of the site. That happens whether they are logged into Joomla through their Joomla credentials or through JFBConnect/Facebook.
The remember me option will automatically log the user back in if they revisit the page after their session has timed out. If you enable the "Automatically log facebook users in" setting in JFBConnect, that will also re-log the user in if their session timed out and they are still logged into Facebook.
So, there's no way for the user to choose that option, but you can still have the same effect with the Auto-login feature of JFBConnect.
Hope that helps explain,
Alex