Pretty much the theory we agreed on in the old thread.
Modern computers have energy-saving measures as well: the screen turns off, the harddrives power down, etc. All in an effort to save electricity when the PC is left passive for a couple of minutes. I'd imagine they'll be infinetely more advanced in 1000 years.
If everything else fails I'm sure Bender could store all his memories and knowledge on a permanent storage thingy (like a HD) and shut down completely. Leela hitting him with the showel prompted him to reactivate.