Firefox Portable

The internal Firefox updater will work within Firefox Portable but there are some caveats. First, it will only update the bit version for the OS you are currently on. Firefox Portable includes both the 32-bit and 64-bit version, so if you're on 64-bit Windows, only the 64-bit half will be updated. Second, the FirefoxPortable.exe launcher won't get updated, so you'll be missing out on portablization improvements and bug fixes (missed files as things change within Firefox, etc). Third, the updater will leave some non-personal files behind.

The best way to update is via the PortableApps.com Platform's updater as the majority of users do. The second best way is via a manual update within the PA.c Platform. The third best way is to perform a manual standalone update as described here to ensure you get the updates to the entire thing (32-bit and 64-bit as well as the launcher): https://portableapps.com/support/portable_app#upgrading