Excessive heat - which is caused by excessive current - which is (as I understand) often caused by a short circuit in the rectifier/regulator.
My non-professional opinion....
The R/R is the "weak link" as it has the most parts that CAN fail. Stators by themselves rarely fail because they are just a bit of metal with wire wrapped around it. The R/R on the other hand is full of bits and pieces that all need to work correctly. Besides the Diode Bridge, there are 18 other electrical components in the schematic I posted. Most likely to fail is the Diode Bridge (no charging) or the SCR (Shorts to ground, creating tons of heat). If the Stator is melting, which would be an incredible amount of heat, or just getting hot enough that the wire covering melts....covering is rated to ~133 C, or 271 F, it would most likely be because the R/R is not shorting the power to ground correctly.
Thanks for this informative thread. I am with you, I want to understand this so I can prevent stator #4 failure when I am several days away from home. I think this is understandable so far. I understand electrical theory enough to be dangerous but not enough to solve this.
Here are questions. As the stator operates, what happens to the stator when the power demand or resistance of the R/R is excessively high or low? Would either condition heat the stator?
At a given rpm does the stator put out a constant wattage or is it dependent on the R/R resistance.
I would guess the R/R resistance or draw from the stator should be fairly constant and what power is not used by the bike is wasted in heating the R/R. As the bike draws more current there would be less heat at the R/R and when the bike draws more current (amps) than available the system voltage would drop.