I have noticed with my SHIELD Android TV that occasionally I will have no connectivity, if I scroll to my network it will have the no connection message. Restarting the SHIELD takes care of this, but it's super annoying. SHIELD is connected to a switch on my entertainment stand, which is connected to my main router/switch upstairs all via cat5e. I don't know if this is a DHCP issue or something else but it appears to happen after device has been in standby. Anyone else having similar issues or suggestions? I don't have a static IP set for the device, and my router handles DHCP. 5 port switch it's hooked to directly doesn't appear to be having any issues with other devices.
Anything else on that switch having issues? Try swapping out cable. Try different port on the switch. Try assigning a static IP to the shield. If static IP fixes it, might have to extend the lease time on DHCP addresses on your router. Also make sure there are enough DHCP IPs available for the amount of devices you have on your network.
Based on the info provided, that's where I would start.
EDIT: Also own a Shield; no network issues. Setup is similar to yours. Shield -> gigabit switch -> wifi router.