Some firefox users had problem with so-called "accellerators" extensions... most of them try to download the linked pages before people actually click on them.
Unfortunately one of the links in Web Control Panel is the Log-out one...
If you have one of such extension, try disabling it or, if configurable, instruct it not to prefetch your aMuleWeb addresses.
And of course... you must have cookies enabled for the new aMuleWeb to work correctly (there's no more a session ID in the url), so may be worth a try to check that your aMuleWeb address isn't listed as "block" even if cookies are enabled (just to be sure).