When the resistor gets hot, it't still working. At rated power, surface temperature will be quite large (e.g. 150°C) and the resistor possibly looks a bit "burned". You should be able to measure the resistance when the device is switched-off.the resistor does get quite hot and at the sides of the resistor where the wires come out, i can see brown calcification and a bit on top of it. The circuit does turn off time to time and I am just wondering if the resistor could be causing it to?
The resistors you show, will going open in case of overload. Then they are dead. They will not sometimes function and the not.