I took apart the old, failed switch.
There is a thin copper wire bent in a sort of upside-down W shape. The shorter rear end of this swings back and forth in a little molded indentation in the tail end of the blue plastic actuator. The longer front end of this W goes up and over the top of the copper spring, down through the copper spring (see the tiny hole) and then down into the long center slot in the top of the blue plastic actuator. This longer end of the W essentially stays still because of the tiny hole in the spring holding it in place.
It looks like the blue plastic either melted or wore out in the indentation at the tail end so that the copper wire's end no longer toggles back and forth. What this means is that people can't open up their original, failed switch and repair it, then put it back in the router.
This view is of the top of the blue actuator.
When the switch is assembled, you can see the tiny hole in the copper spring and the longer end of the W wire at the vertex of the V-shaped hole in the top of the housing but not much more.
The genuine E-Switch is rated for 85 deg. C, but I measured the temperature of the switch and found that it sits around 48 deg. C. (Ambient temp is around 20 deg. C.)
But I know that I didn't press the button very often, so it is more likely that the failure was due to melting rather than wear. The genuine E-Switch is rated for 10,000 cycles. The failed switch might never have been cycled more than 200 times in its entire life, but it has sat there for 3 years straight, 24-7, through some really hot summers.
Perhaps the old switch was made with a far inferior plastic that failed at much less than 85 deg. C, but I find that hard to believe. Most of the industrial plastics would never melt anywhere as low as 50 deg. C. And if the interior had gotten very, very hot, the router's plastic housing should have at least warped.
This would suggest that it was mechanical wear, but again, I didn't press this button nearly enough to wear it out.
I did not take apart a genuine E-Switch to see if the failed one had changed the mechanical design. That's a possibility, that they cheated and cut some corners on the actual latching mechanism.
Strange problem inside the switch that will probably never be diagnosed.