I looked, but found nothing like an "inactivity timer" in the menu.
It occurred to me that dishnet customers in the US had likely encountered this, so I searched at tivocommunity.com. I found a workaround posted there - in the receiver, set up a timer to go off around 4AM everynight and set it to last 23 hours. I set this up last night, so I'll see how well it works.
The downside to this is that the receiver will change the channel at 4AM, so if the tivo is recording then, you'll get the wrong show. I typically don't record things at 4AM, so shouldn't be a big problem for me.