If you only lost power, then Mysa will automatically reconnect to the internet and reset its internal clock. In this case all of your settings will resume when the power returns.
If you only lost internet, then Mysa will continue with your schedules and settings as normal. The only difference is that you can't control the thermostat from your phone. Due to the lack of connection, you will have to use the buttons on the thermostat's display until the internet comes back.
If you lost both internet and power, then Mysa will continue trying to re-establish a connection. Until a connection is found Mysa will maintain the setpoint temperature when the device lost it's connection.