Well, it can't ever completely shut down since there is no physical switch (the reset button notwithstanding
) It will always need to use some power to check on the "menu" sensor to register a press to turn on the device, at the firmware level though, not the actual OS(?)
Though I don't know why yours would be down to empty from a full charge overnight. I had mine off for several days, and it barely made a dent in my battery life... unless on yours some hung process kept running full speed, or the battery indicator is way off.
You can try a full reset (keep holding several seconds), preferably without the SD card in, in case there is some conflict between the internal registry and the settings stored on the card) Then try again with a full charge overnight.