When I worked at AUDI some years ago.. the reason resistors burnt out was the elements became corroded and used tons more current
The big one was the internal heating fan.. Remember these things are designed to be just so. ie there is no room for maneuver.. If its a 3W resistor just work out how much current flow there is. The switching transistor ( looks like a t220 device) will also be working too hard 3W is a few amps at 12v that's if the mirror circuit is. power, element, resistor, ground.