Is the "external drive" connected via USB, firewire, or thunderbolt?
If it's a USB drive, you probably are NOT going to be able to update the firmware so long as the drive is in a USB enclosure.
I will take a _guess_ that most (if not all) utilities to update firmware are "looking for" a drive that's mounted internally (connected to the SATA bus). They just aren't programmed to "find" a drive mounted in a USB enclosure.
Probably the same for firewire.
I believe that if the drive is in a thunderbolt enclosure, _some_ utilities might work (they will "see" the drive as being attached to the PCI bus?).