If I edit a device templates thresholds and change the Consecutive Times form the default value of 1, click OK and then re-editing shows that it is still the value of '1'.  Change value, Click OK and immediate Associate to devices (i.e. without re-editing), checking the monitor for the given device(s) shows its still the value of '1'.

If I change the value directly from the devices Monitors screen and save, the change sticks.

Result, I have to manually edit every process monitor individual per device that I want to have a 'Consecutive Times'  value other than '1'