On the old series 1's there was a problem with upgrades which may or may not apply to the newer series 2 directivos. Perhaps someone more in tune with how the newer models work could opine.
On the older tivo's, there were two partitions that the operating system used, one for the 'current' software and one for an upgrade version. I believe the intent was that if the upgrade version didnt download or install correctly, the tivo could boot back to its former image. On the next upgrade, the download would go to the 'old' partition and the two partitions would swap who was 'active' on each download.
Problems came about when one of the partitions wasnt used for a long time, then a new s/w image was downloaded to it, no problems were immediately detected, but the new area was a so-so portion of the disk and progressively got worse. You'd get reboots, freezes, slowness and all sorts of similar sounding stuff.
Seems the trouble originated from the manufacturer writing the image to the disk and not testing the unused areas.
The solution then was to try to copy your disk contents to a new, non flakey drive and hope you could get everything off of it, or install a fresh new drive with a clean copy of the tivo s/w.