I was also surprised that my camera didn't have the feature. To get an idea what settings I have to work with on the camera, the menu layout looks exactly like this guy's menu:
viewtopic.php?f=2&t=47
except his firmware is a New Orange Menu version number.
The most relevant looking item is of course "AUTO POWER OFF" but that definitely doesn't do what I'm looking for.
Sabe, good to know that there is some hope for me.
For what it's worth, here are pictures of the box and stuff.
http://i.imgur.com/6zgJKUs.jpg
http://i.imgur.com/3BaHIkn.jpg
http://i.imgur.com/A5kocn1.jpg
And the included player software looks like this:
http://i.imgur.com/6oMjrEv.png