First off, I'd highly, highly recommend upgrading your Joomla installation. 1.5.7 is over 2 years old, and there's been 15 updated releases since then. JFBConnect should work with that old of a version, but it's only been tested for 1.5.11+ compatibility.
As for your issue, I tried to log in, and can see what you mention. Can you try using the JFBCLogin module not through a pop-up, and see if that works? I'm not sure what that pop-up is doing, but it could be interfering with the Javascript communication required between your site and Facebook.
One other possible cause is the use of the Share button. Facebook has deprecated the share button, and it's use can actually conflict with Facebook's most recent Javascript libraries (which we use). If you can try testing with the share button disabled (or on a page that doesn't have the share button), please do so.
Let us know if any of the above helps. We'll do what we can to help you solve the problem.