DIAGNOSIS This is usually a Wi-Fi router issue, not a thermostat issue. The Ecobee has a modest Wi-Fi radio, and it can struggle with weak signals or router settings that aggressively drop idle connections.
FIX Start with the simplest router fix. Log into your router's admin page (often 192.168.1.1). Look for a setting called 'AP Isolation', 'Client Isolation', or 'Wireless Isolation'. Make sure it is DISABLED. This setting prevents devices on Wi-Fi from talking to each other, which breaks the thermostat's connection to your phone on the same network. Also, check if you have 'Smart Connect' or band steering that switches devices between 2.4GHz and 5GHz. The Ecobee only uses 2.4GHz. Try setting it to connect to your 2.4GHz network specifically.
IF THAT DIDN'T WORK The signal might be weak. Your furnace closet or hallway might be a Wi-Fi dead zone. You can check signal strength on the thermostat itself: go to Menu > Settings > About > Wi-Fi. It will show the signal level. If it's 'Poor', consider a Wi-Fi extender that plugs into an outlet closer to the thermostat to boost the 2.4GHz signal.
HEADS UP Avoid putting the thermostat in a 'DMZ' or assigning it a static IP unless you really know what you're doing. Let your router's DHCP handle it. The Ecobee is pretty good at reconnecting if the router just gets rebooted occasionally.