The most common problem with a TRV is that the valve sticks or catches. This means that they are either stuck open or closed. This will happen when the setting has not been moved for some time, such as after the summer.
If you cannot get the plunger working again, then the valve has failed and will need to be replaced completely. See below section on how to change a TRV for help with this.
The second problem that can occur is that the thermostat can fail. If the valve is working, and the plunger is moving freely, it is likely that the thermostat is not depressing and releasing the plunger, therefore opening and closing valve as it should. The thermostats is relatively simple which uses a trapped bubble of gas, liquid or wax to expand and contract with the change in temperature of the room to move the plunger.
Solution and Maintenance: If the thermostat has stopped working there is nothing you can do except replace it. Before you do buy a new one it is worth making sure that this is the problem, but swapping the thermostat with a working TRV and confirming that the valve now works.
For general maintenance of your TRV it is worth opening and closing the TRV fully several times to get the mechanism working. Do this several times per year to stop the plunger or piston seizing up.