DIAGNOSIS The thermostat has a local connection to your HVAC, but its communication link back to Honeywell's servers (and thus your app) is broken. This is almost always a problem with your home's internet connection or the thermostat's specific network path.
FIX Don't touch the thermostat first. Reboot your home internet. Unplug your modem and router, wait 30 seconds, plug the modem back in, wait for it to fully boot, then plug the router back in. Give it a few minutes, then check the app. This clears router glitches that can drop specific device connections. Also, check if your internet service is actually up during these outages.
IF THAT DIDN'T WORK The thermostat's own network module might need a kick. On the device, go to Menu > Wi-Fi > Network Status. If it shows connected, choose 'Clear Network' anyway, then go through the setup process to rejoin your Wi-Fi. This forces a fresh handshake with your router.
HEADS UP The Total Connect Comfort app/servers have occasional outages, but they're rare. Before you spend an hour troubleshooting your gear, check Honeywell's service status page online or a site like Downdetector to see if it's on their end.