1. It's not the remote
I use a Logitech Harmony One remote for my entire setup and the Harmony controls all other devices just fine. Only the DVR had problems, so I know it was not the remote. Just to be sure, I tried the manufacturer's remote when the problem occurred and the problem did not go away with the use of a different remote.
2. It's not the DVR
I did some research online that suggests that that there might be infrared light coming from somewhere else in the room that is interfering with the receiver. Possbile sources of this IR light include: Daylight, CFL Bulbs, LCD TVs. Since the problem happened at night, I know it wasn't daylight. It also happened even when there were no lights turned on in the room. So I tried turning off the TV. Problem went away instantly. Wait a minute, what?
3. Something about the TV
If it is the TV, why does it not happen at all sometimes? I researched some more and found that LCD TVs can emit a lot of IR light when they are "warming up." In my case it was my backlight reaching full brightness. Most LCD TVs, except for those marketed as "LED TVs" use a compact fluorescent bulb that goes all the way around the edge of the TV as a backlight. Apparently, this backlight can take a few minutes to reach full brightness. And during this time, there is a ton of infrared light leaking out of the display. It's been referred to online as the "IR leaking" phenomenon.
4. Why now?
I couldn't imagine that the problem would just start happening all of a sudden. For almost a year I have not had a single issue with this DVR. On one online AV forum I read a suggestion to try adjusting the backlight brightness. That's when I remembered that a couple of months ago I calibrated my TV for the best picture using the Digital Video Essentials HD Basics Blu-Ray disc. As part of the calibration I had turned my backlight brightness down from 50% to about 30%. That must be what caused this problem to suddenly appear.
5. The fix
When I had just turned everything on, and the DVR was not responding due to the backlight warming up, I opened up the TV settings and adjusted the backlight brightness. I kept trying the DVR remote and it started working consistently as soon as I reached about 40% brightness. I put it back to 50% just for good measure. This fixed the problem. Now I can hit the "watch TV" activity on my Harmony remote and everything gets turned on and I can control the DVR right away without getting the interference from the TV.
6. Bottom line
I have a Vizio VO32LF which is a 32 inch Full HDTV. Apparently when the TV is properly calibrated, it leaks IR light for the first 20-30 minutes which interferes with my DirecTV DVR. I imagine that other devices might be susceptible as well but I haven't personally seen it. This problem is not unique to this TV either, as other people have reported that they have this problem with other brand / model TVs. I have read that it can even happen with plasma TVs. LED TVs seem to be immune to this problem from what I have learned.