There's a bug in Firefox 32, that some tabs miss the favicons: https://bugzilla.mozilla.org/show_bug.cgi?id=1061456
The bug is caused by the introduction of the new cache and shows up in case pref "browser.cache.disk.enable" is set to "0" and "browser.cache.disk.smart_size.enabled" set to "false".
IIRC, the portable container for firefox sets those values forcefully, that's why I'm writing this here.
The bug seems to be gone if pref "browser.cache.disk.enable" is set to "false", so it would be nice if FirefoxPortable container would forcefully assign that value to that pref.
It does not set either of those value forcefully. It just has browser.cache.disk.capacity set to 0 by default. The same as if you open Options and set it to 0. An end user can easily change that through the UI.
This is a bug in Firefox proper. If it's actually a full bug that affects multiple sites, it will be fixed in an upcoming release. Setting browser.cache.disk.enable to false is not an option as that would require the end user to open about:config which is a non-starter.
Sometimes, the impossible can become possible, if you're awesome!