The reason for this behavior is to prevent a service call for a DVR that is corrupted by software only.

Basically there is a counter on the hard disk that counts the number of failed reboots.  When the box first powers up, the counter is immediately incremented, usually from 0 to 1.  After the box is fully started up and running, it runs some self-tests internally, and if everything checks out, then it resets the counter to 0.

If the box fails to start up for whatever reason, the counter never gets reset to 0 and stays at 1.  If the box is then unplugged to attempt a reboot again, the first thing the box does is increment the counter, now from 1 to 2.

If the counter ever reaches 4, the box assumes that the past 3 reboots have failed to get fully up and running and pass a self-test, and it needs to perform a disaster recovery -- format the hard disk, download a fresh installation of the OS, and try again.

Because your power failures occurred in succession with a period between the failures of less than the time required for the box to start up, the box never got to the point where it was fully started up and a valid self-test was run, so the counter was never reset to 0.  3 successive power failures of this type were interpreted as 3 failed reboots, resulting in the disaster recovery.

This is commonly programmed behavior for computer units that are supposed to be treated as an "appliance".  It is the catch-all for the box to fix itself should it even become necessary.