Should the thermostat lose its Wi-Fi connection, the thermostat will continue to operate as a standalone thermostat.
It will continue to operate using the the last settings it received. So if it was running a program it will continue to run the program.
Once your Wi-Fi is back up and in operation the unit should reconnect on its own
If for some reason it does not reconnect on its own - push the reset button on the thermostat this should reestablish the Wi-Fi connection.