I don't know about DirecTV or HD, but I have Cable w/DVR and CC works fine on recorded shows.

Does CC work while you're watching a live (not recorded) show?

Does it also work while reviewing (re-winding) a live show ?

Yes, we get CC on live shows. Haven't done the reviewing thing.

The display is there on DVDs and live. It's not there when we play anything recorded on the DVR.

I'm thinking the DVR is somehow not capturing the CC, so it can't display it.

It is impossible to get through to DirecTv or I'd be asking them!

What is the model number of your Directv HD DVR? Is there an option for turning CC on?
I've read on some of the satellite TV forums that several of the HD channels weren't passing CC and that Directv was working on it.

I have Dish and it's an option on the DVR menu to turn CC on and off. I've had to use it a couple of times when a recorded program loses sound for some reason. Direct probably has the same feature.