What you describe sounds like a caching or optimization issue that may not be storing the session cookie properly on your site.
Can you let me know:
* Does the same thing happen if users try to login using their Joomla credentials?
* What version of JFBConnect are you using?
* What version of Joomla are you using?
Finally, please post from the account that you subscribed to JFBConnect from. Priority support is for our active subscribers.
Thanks,
Alex