I'm kinda baffled by this. I tried testing it in multiple browsers across multiple computers (including FF3 and FF5, the two that are mentioned here), but I can't get it to fail.
My best guess right now is that you might have a problem with the cookies stored on your computer. Clearing your ZAM & Allakhazam cookies might fix the problem. That will reset any other cookie options you have saved, and you'll be logged out of the site by doing so. To delete just these cookies go to your Firefox options, and under the Privacy tab click "remove individual cookies" and search for "zam.com". That should display all ZAM and Allakhazam cookies, which you can then remove.