DIAGNOSIS: This is typically a conflict with your router's band steering or a weak Wi-Fi signal at the thermostat location. The Enhanced model can be fussy with certain router settings.
FIX: Log into your router and temporarily disable any "Smart Connect," "Band Steering," or "Wi-Fi Agile Multiband" features. Force your ecobee to connect to your 2.4 GHz network only (it doesn't support 5 GHz). You may need to create a separate 2.4 GHz SSID for it to connect to reliably.
IF THAT DIDN'T WORK: The issue could be IP address related. In your router settings, assign a static IP address or DHCP reservation to your ecobee's MAC address (found in Settings > About > Network on the thermostat).
HEADS UP: If your thermostat is on a wall that has plumbing or ductwork, the signal can be blocked. Consider a Wi-Fi extender if the RSSI value in the thermostat's network settings is below -70.