If the tweeter itself was open circuit due to heat expansion of diaphragm breaking the diaphragm conductor then it should cool down when it stops playing and fix itself, turning on and off continuously. I'd love to see that! I don't think this phenomenon would last long since the diaphragm is so thin and delicate. But since it stays off until you disconnect the speaker cable, that suggests to me that something in the tweeter crossover is shorting to ground (electrically muting the tweeter) when heated, and the heating is sustained as long as current is applied. It doesn't cool down and stop shorting until after current is removed by disconnecting the SC.
A resistor is most suspect because resistor's job is to create heat but an internal short can be in any component. Feel if any tweeter crossover parts are warm to the touch when signal still being played after the tweeter goes quiet. If there's a short it should be warm. Turn volume up to normal-loudish level to enhance the heating so you can feel it. Do you have an IR camera?
Astrologically, Mercury (and Pluto) are retrograde now, so things will break in the most confounding and unimaginable ways.
