A
Kindle Review on Amazon by P. FEng indicates that the Kindle will quickly drain its battery (1-2 hours) if you don't turn off the wireless on a plane. This is plausible, since my phone drained quickly in Canada as it tried to find service that was not available. Assuming this isn't an isolated hardware fault, it is a warning to everyone to be careful when traveling.
I agree with P. FEng that this may be is a design fault. A cell phone needs to be on to receive incoming calls. A Kindle does not need to be connected all the time, and it should have good power management for the wireless connection. I would also have allowed charging via USB, although this lack may be a consequence of the long design cycle (USB charging was less common even a year ago).