It's quite hard to design anything with a supercap to run for more than a few weeks between charges. Bigger caps tend to have a higher self-discharge rate too, so although a bigger cap can supply a larger current for a given period, they're unlikely to be able to supply any given load for a much longer period.
Besides, if that were the case, every scope would fail after a few weeks' disuse, and I know first hand that they don't.
I'm going with the NAND data retention idea, which would tie up with the relatively recent - if vague - firmware updates we've seen.