So, as luck would have it, I was minding my own business watching US Open Tennis on Universal HD when the picture went blank! ALL my cable channels went dark. This was the case with my first CableCARD (the one I'm using now is my second), I got the broadcast channels in SD and HD but no cable channels.
I called TWC, they "hit" the card, I turned off the 5070, pulled the CC, turned on the set, reseated the CC, turned off the set, turned it back on to reboot the card. All is well!
The moral of the story is: be prepared to do this sort of stuff when you have a CC. I STILL think it's worth it (even though I was cursing out the CC and TWC today). If the "hit" didn't work, I was ready to march over to the cable company and pick up a STB/DVR. I still might get a DVR, but I want to keep the CC.