None of mine do this. When powered down, the ethernet ports are completely dead. The lights on the network switch go off; no one is home. They wouldn’t be able to keep the NAS up in this state.
One of my three units is Wireless. When I turn that unit off, the USB interface goes dark. All lights go off.
Yeah, I’m with Tony (and, very oddly, our setup is disturbingly similar – two older Lives, one Plus, and one accessed wireless). My NAS spins down even with the Lives are working (if they aren’t playing anything). And pretty obviously, when they are turned off there is zero access to the NAS.
Now, I access the NAS through net shares, and not a media player, so perhaps that’s the issue.