They are really not turned off completely. Most go into a low power mode. This is usually to maintain the wireless connection, so that they do have to restart the initial setup. Imagine your phone turned off every time you locked your screen and you have to wait for it to ‘boot up’.
The battery in itself can’t hold the same level of power forever, the potential energy to drive the current trickles down. It’s like a leaky water bottle, it will slowly discharge even when not in use.
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