A strange one, this... it seems to have happened over the weekend, during which I made no changes to anything, but at some point DABDig lost the ability to start DigiTV for recordings. It was still able to start it to Listen, just not to Record.
Using TRACEFLAGS=4, I found that DABDig was trying to start DigiTV-HD.exe, instead of DigiTV.exe. So I've cured this by editing the "NEBULADIGITVTASK=DigiTV-HD.exe,DigiTV.exe" line in dabdig.ini to remove the former filename.
So it's all working fine again now; but it's still a puzzle why, after having been working perfectly well, DABDig should have suddenly been trying to start the wrong program - but only for recording, not for listening.