$0.02 FWIW (i don't charge for this drivel.
Pucks caution is noteworthy for safety, but I don't think it is a heat related problem. Excess current would likely "weld" the appliance module contacts closed. Huge amounts of current overload would be needed to overheat the relay contacts. I come nearer thinking it is a noise problem generated by the lights, although the 2 hour time window throws a big question mark into that theory.
Do you use X10 elsewhere (non holiday) in the house? If so, assumably everything works fine - all the time? If you don't have X10 elsewhere: does anything else in the house get turned on in the time frame the appliance module decides to go on strike?
As a test; try waiting long enough that you are sure the appliance module will not work. Go out and unplug the lights and have someone immediately use the SC503 to turn OFF the appliance. If it clicks, it probably isn't a heat problem. Turn the module back ON, plug in the lights and see if it will still turn OFF. If it doesn't click OFF, have someone cycle the appliance module while you unplug lights, one string at a time until it works again. (Walkie Talkies will help with this).