Yes, the server is connected to the router via Ethernet cable. My player is connected to a travel router via Ethernet (and the travel router is wireless to the main router). I haven't noticed any dropouts. The connection problems I have had are the server not being able to mount the NAS or the server and player not connecting (LMS not responding to the broadcasted message by the client?). I do think that reserving IP addresses would help, but when I tried it recently I couldn't get it working. I may try again when I have a minute or if the problem occurs again.
I used to have my modem and router on a UPS because we do lose power fairly often. I don't think that power loss has been the cause of my problems, but short glitches might be. My UPS died after what seemed like a fairly short time to me (a few years?) and at that time I was looking into getting a good sized battery backup for my home so I didn't replace it. Now, I'm leaning towards waiting to see if sodium ion batteries hit the market soon to purchase the battery backup so I should probably go ahead and get another UPS.
All my local music files are on the one ASUSSTOR NAS, so power to those drives is good as long as my home power is up.