What if the thermostat screen turns off and lights up intermittently?
If the display of the device is completely off, it is possible that the thermal protection is activated or that the device itself is broken. Tripping of thermal protection can occur when the heater overheats or when it is obstructed by an object (curtain, furniture, etc.). The power to the baseboard and the thermostat is then cut to prevent fires. You should, therefore check if your heater is obstructed by an object. Some electric baseboards diffuse heat less well if they are not perfectly installed to the wall.
Also, depending on the power of the heating system, the size of the room and the outside temperature, the heating unit may not be able to maintain the set temperature, causing overheating. If possible, swap your thermostat with another working thermostat that allows you to check if the problem is local or if it is caused by the device. If the issue remains even after you have interchanged the thermostats, contact an electrician to verify if the problem is caused by your heating system.