Hello,
I have the exact same problem, when i try to login using facebook botton, it shows popup where i enter mail adress and password, then it disappeard, and then like nothing happened, if i connect to facebook i am already logged in, but in my website, it is not working, i did not have any message like you are logged in using facebook credentials, and it is like i never logged in.
When i try again to log using facebook, it shows only pop up and disappears.
I have also jfbconnect.js in my template, all cache is desactivated, and i can't see any error message when pop up disappeard.
Please help me solving the issue. thanks a lot