DIAGNOSIS The eero isn't detecting a stable Ethernet connection from the satellite node to the main gateway or switch, so it falls back to a wireless connection.
FIX Check your physical connections in this order: 1) Use the cable that came with the eero or a known-good Cat5e/Cat6 cable. 2) Plug one end directly into a LAN port on the gateway eero or your switch, and the other directly into the WAN port on the satellite eero. 3) Restart both eeros after connecting the cable.
IF THAT DIDN'T WORK Your network might have a loop (more than one cable connecting two switches/eeros). Ensure there is only one Ethernet path from the satellite to the main gateway. Disconnect all other cables from the satellite except the one intended for backhaul.
HEADS UP It can take up to 10 minutes for the eero app to update and show the "wired" connection icon. Be patient and don't unplug cables during this time.