JW,
I can't login to the page to begin with, actually. I'm seeing a few strange things, and they all could be related to your logout issue.. or could just be something different.
When I go to the page you posted, first off, there's no Login With Facebook button. When I click the Login link in the middle menu, I do go to a page with Login With FB text. However, the button isn't visible. There are some Javascript errors with Facebook's Javascript library that we've never seen before. Can you let me know if this is a new FB application, or an old one? Also, if you go through the Autotune section of JFBConnect for the Facebook Application, are most of the recommendations set.. mainly for Website URL and App Domain?
So, without the button being there, I can't click it to actually log in.
Another odd thing is that your site seems to be linking to an IP Address. I'm assuming you're aware of this, and I don't think it's causing the problem.. however, it's possible if there's some weird configuration going on that it's part of the issue.
Please let me know if the /login page is the right place to login, and if not, where I should. If you're seeing something different, or the same, let me know. It's always possible its just a hitch with Facebook itself.
Thanks,
Alex