Yowser! Alright. We have a solution that should fix the issues above. Basically, Facebook looks to have introduced a (few) bugs recently into it's Javascript API. It's affecting a non-negligible amount of sites in that the 'logging in' event can be triggered on every page load. We use that event for auto-login functionality, but only expect it once, as their documentation states.
We have a workaround that will be in the 4.2.4 release that will be out anywhere from late tonight through Wednesday afternoon, depending on how testing goes. The new method will set a cookie stating if auto-logging in has already occurred and if so, will prevent another auto-login for however long your session is set for. It's not foolproof as the user could be logged back in if they browse your website for a while after they login, but it should be good.
Morpheus, I've implemented the fix on your site. It seems to work, but honestly, you know exactly what you're looking for, so please test. This is with the authResponseChanged code, so it should work as you want. We're still making minor mods to the code, but it will be very similar to what we did for you, so let us know if there are problems!
Thanks for your patience everyone, and hopefully auto-login functionality won't cause issues for you after the 4.2.4 release is out!
Alex