Since the ecobee receives its weather data via Wi-Fi, in a scenario where your thermostat's Wi-Fi connection is lost, the ecobee will engage your heat pump and still operate as normal in an attempt to satisfy your set point.
During the first hour, the temperatures are recorded to determine if the indoor temperature is rising by at least 0.5F. During the second hour of operation, the indoor temperatures are measured as well. If the temperature has dropped 0.5F or greater by the end of the two hour period, the heat pump will be locked out until 12:00 PM the next day. This is based on the assumption that 12:00 PM is the warmest part of the day, and re-engaging the heat pump will carry the least amount of risk. Once the heat pump re-engages, the same run time protocol will apply if Wi-Fi is still disconnected and the ecobee is unable to access weather data.
You can turn the system mode on the thermostat to "Off," then back to "Heat" to reset the heat pump lockout "flag" anytime during the heat pump lockout period.
Note: The ecobee will engage your auxiliary heat the entire time the heat pump is locked out and your set point is not satisfied.