Check the Social -> Misc section of JFBConnect for the "Admin Render Key" setting. If a value is in there, you need to use the tag like {JFBCLike key=1234} (where 1234 is the key you've set).
If that's not it, try disabling any caching you have enabled, particularly the System - Cache plugin. If turning that off fixes things, let us know and we can help you to re-enable it.
Thanks,
Alex