I would think a common sense appoach makes sense, just like with a PC. If your using it all the time, then go ahead and keep it on, no point booting up/powering down all the time. At the same time, if your not going to be using it for a few days, doesn't make much sense to leave it on really. If I'm on vacation for a week, I turn my PC and other stuff off, same with the Axe.
I don't turn it off when I go to eat lunch as I'll be back in an hour or so, but if I'm done playing for the day and maybe won't get back to it for another day, I power it down, along with my monitors, wireless etc.
Heck, same goes for the lights in the room lol