You're right that it may not be worth the time and effort to figure out what the bad ESC is thinking, Mike -- but we hate an unsolved mystery!
It seems that whatever the timers are currently putting out doesn't satisfy this ESC. These microcontrollers are stable enough that I wouldn't expect it to change its arming pulse width significantly over time--and it didn't work with other timers, either.
That does point to the ESC as suddenly wanting something different. Since the throttle trim does affect the width of the arming pulse (throttle off), the only in situ experiment (for John!) that I can think of is to see if throttle trim affects the ability of the radio to arm the ESC.
If you wants to pursue the matter, perhaps just for the sake of science, John, you could send the ESC to Mike or me, and we could use a throttle emulator to try to make it run a motor.