My answer is not definitive or conclusive, but I would recommend you check al the menus in the DVR. I know that in NTSC (which is the composite or SVHS) the captions are sent during the vertical interval. You used to be able to see them if you had a vertical hold control. Now it takes either a modification or a scope with dual time base.

With HDMI there may be a whole different scheme. It is not sso much the higher resolution that makes me think that, it is possibly other information that maty have crowded it out and now it is sent some other way. Simply not being interlaced would change the scheme of things. Or maybe the DVR generates it instead of the TV, I do not know but it is possible. If so, remember that if you were to copy it the CC would be one the screen in the dubbed recording.

So, look at all the menus, if you do not find anything it may be a limitation of the system.

Question : Are you simply using the DVR tuner straight off the air ? There is no convertor box ?

Another thing you might consider is seeing how good it looks using SVHS/SVIDEO. It does make a difference. Just not going through the COMB filter helps. It might be good enough because not all OTA material is really high resolution. when they split one channel into four, it is not quite the highest, like watching a movie at the theater. Between the line doubler and the enhanced video bandwidth it might look good enough.