I just tested on your site with both a Facebook account and logging in with a normal Joomla account. In both cases, if I reload the page repeatedly, sometimes the map will show and sometimes it will not.
I don't think this is related to JFBConnect. Try again to make sure if you refresh the page multiple times that it always works for you when logged in as a normal Joomla user. If not, I'd recommend contacting the map extension provider.
I hope that helps,