To be clear, when the Potterton programmer is in the OFF position, the thermostat won't work. Only when the programmer slider is in the ON position, will the thermostat work. I'm sure that you have already realised this.
It is my opinion from what you have described that if you have the programmer set to OFF, but the relay box green light is ON, then the relay box has theoretically received a signal from the thermostat (a flame symbol) because it wants the boiler to be firing as the room temperature is too low. However, because you have the programmer OFF, the boiler is unable to fire and the boiler is OFF. You have overridden the thermostat with the programmer. Therefore, nothing happens and the thermostat is unable to reach the target temperature of the thermostat and it is stuck like this with the green light on, trying in vain. This is my explanation as to why you are seeing the green light on the relay box "permanently" and why it tests out OK with Honeywell on the telephone when testing simply increasing and decreasing the temperature explained earlier (whilst the programmer is ON).
So, it is my belief now that the green light on the relay box is a red herring as the correct operation has been proved. The only thing that has not been proved indefinitely is with the thermostat in the normal room location whether the signal is OK, but again, if there were an issue with that, then the red light would be lit on the relay box. The red light lights up if a signal has not been received in the last hour. You also say that the thermostat is in the room below the loft and used to work OK. So I doubt that this is a problem.
So, your house goes through swings of cold periods losing heat. Your original question actually was....the thermostat works to bring the temperature up to the target room temperature. However, the thermostat does not seem to be triggering again when the thermostat drops by a few degrees.
So lets focus on troubleshooting that fault and ignore the relay box green light: Where is the boiler located? You need to be looking out for what happens when the target room temperature is reached and then when the temperature drops by a few degrees (still keeping the programmer ON during this period), does the flame symbol on the thermostat come on again? does the boiler fire up? at what temperature does the boiler eventually fire up? and what is the target temperature set to?