So I thought I'd update on what I've been through... As a refresher, I had a HR 44 Genie installed last month and when programming the "new" RC71 remote, it would work on my primary TV a few times then forget the "turn TV on" code. Everything else would work fine, it just wouldn't turn the TV on (it would turn the TV off though). I tried resetting the remote and programming it in both IR and RF modes, with the same results. I finally got DTV to send me a new remote figuring it had to be a firmware issue. Nope, same results. I then purchased a RC65 remote to try.
Amazingly, it gets even weirder (for me anyway).
After programming the RC65, again everything worked as it should for a little while. Now, if I have the selector switch set to DirecTV and press the DTV & TV power on button, the Genie comes on, but not the TV. Once they are on, if I hit the power off button, it will turn everything off (including the TV). However, if I slide the selector switch over to "TV" it does turn the TV on!
Again, annoying but workable - sheesh, I've pretty much resigned myself that it's the TV, not the remote (though I've never had this happen before, and the bedroom TV is even older but the RC71 works fine in there)