Good news. We found the issue on your site. It was with JFBConnect, but I can't say we still fully understand the issue. We've implemented a work-around and things should operate as normal on your site.
The problem dealt with our logic to decide if a 2nd Facebook permission window should show. On your site, it never will, so we disabled this check.
Please test. In the process, we disabled and re-enabled many plugins and modules, we changed your template a few times. All were in an attempt to 'not blame us' and find a conflict with some other extension. We didn't
Everything should be just as we found it, but let us know if it isn't, or enable whatever we disabled.
Just so you know, we installed the "JFBConnect System Plugin" which will be a part of the 3.0 stable release. You're getting it early. No new features or anything exciting, just wanted to point it out in case you notice it.
When 3.0 stable does come out, we'll try to have a fix for this issue. However, since we can't recreate this problem on our development servers, it's possible the problem may still exist. If so, let us know, and we'll fix it much quicker next time.
Thanks!