Posting this in the hopes it saves someone else some time:

Problem: DirectTV box mysteriously started powering itself off starting sometime during the week of 2/13/2012.

Cause: DirecTV pushed a new firmware update out that enables a PowerSaving mode that turns the box off automatically after a certain period of inactivity (no buttons being pressed).

Solution: Using the receivers built in menu, disable it. On the remote, hit the 'Menu' button, then select 'Settings & Help' -> 'Settings' -> 'Power Saving' and disable it.

Like most people I thought my box was going bad and called it in. The very helpful DirecTV person said no, they had just pushed out a firmware update and they were getting a lot of calls about it. Apparently the receivers have supported this feature for a long time and they just chose recently to enable it.