Okay, like some other, I tried the airport mode overnight. That did make a huge difference. In fact, the battery monitor program I use puts it at 100%.
Overnight, I don't mind switching it to airport mode or even powering down, if I can remember. But during the day, this somewhat defeats the purpose of it being able be in a "sleep mode" and still receive push notifications. I have a couple of different programs that alert me to arrival of new messages.
The other hassle is that I can be doing non-WiFi things in airplane mode, but any time I want to use an app that requires WiFi, I have to first go into settings and switch to WiFi and then back to the app. I then have to remember to do that all again when I am done with that app. This all seems a big step backwards from previous versions.
I have sent in a complaint to Apple and suggest others do the same. I did so here:
http://www.apple.com/feedback/ipodtouch.html