Just to make sure you are posting in the right forum, you're using JFBConnect on Joomla 1.6? Are you using Community Builder, JomSocial, or any of the other profile plugins? Also, please make sure the JFBCSystem, JFBCAuthentication, and JFBCUser plugins are enabled. You can check their status on the JFBConnect Overview page in the admin area.
Hope this helps get started with basic debug. Also, can you post the URL of the page this is happening on, so we can see the results?
Thanks!