Shila,
I just went to your site and registered using Facebook. My account was created as expected. I then logged out and logged back in as expected.
From that quick test, things seemed to work just fine for me. Can you try setting the "Enable Debugging Mode" to "Yes" in the JFBConnect -> Configuration area and try again? Let me know if there are any error messages that appear when you can't login. That will help narrow things down.
Beyond that, please let me know if there are any specific ways to test.. like a specific browser, OS, or anything else that may help narrow things down. We'll gladly help investigate however we can.
Thanks,
Alex