Mine usually goes to sleep after a few hours. I never turn it off except when it freezes up which has been a handful of times and I've owned it for almost a year.
I leave mine on 24/7 on the main screen when not in use, however have to reboot/unplug from time to time due to "connection error". I don't mine leaving it on 24/7, not streaming and the power costs can't be more than 10cents in a month.