Did some searching on the web. Saw someone else that had the same problem and they said they removed the HDD from their xbox360 and then the media center function wouldn't lock up.
I just tried it and it worked great. Watched about 60 minutes of recorded TV on my x360 as an extender and it worked fine the whole time. no lock-ups.
A few more notes. I have 2 xbox 360's. One premium box and one elite box. The lock up occured on both systems so I'm confident it wasn't a hardware issue with the unit(s) themselves. And, I don't think there's anything wrong with the hdd's on the x360s. They work fine for save games and downloaded content (tv shows purchased from xbox live).
Maybe the HDD's have fragmented? But if you can use the media center functionality without the hdd attached to the xbox 360 then what does it even do with the HDD in media center mode when it is attached?
Still all very confusing. Glad I can watch the shows again, but not happy I have to detach the HDD now in order to make it work. I'd still love to get it working the way it used to again.