They're actually designed to be left on. We were actually a bit surprised to see that many people turn them on and off - something they'd probably never do with a normal clock.
I have two chumbys at home that have been on continuously for well over a year - they've only been off when I'm on vacation (or evacuated ) or the power goes out (as it did last night due to a bad storm here in CA).
As I mentioned in another thread, they draw about 2W when on, and the screen in the device isn't the type that would suffer image burnin.