It's a limitation of the game and it is pretty annoying. There's no way to disable a logistics chest. I work around it by assigning it to a different force when it's out of power, but then it's impossible to mine them. Another way to deal with this would be to swap them out with a normal chest when they run out of steam. But that comes with it's own set of challenges like restoring circuits and requests.
Please +1 this bug from the forum to help me out, although I doubt they'll fix them before 2.0 comes out.
https://forums.factorio.com/viewtopic.php?t=111359