I have a 5DMIII with battery grip (by Canon) and Canon batteries. Since a few days ago, I noticed that, all of the sudden, if I leave the camera unused for, say, one day and turned off, when I turn it on, it won't.
I have to change batteries and everything is fine. The batteries that were in the camera seem to have died out because the led of the battery charger blinks once every second.
So I'm not quite sure if the issue is battery (all of them?) or the camera.