There isn't really a test to see if they are failing. Basically you just watch for things like what you are describing as them failing. Update your router to the latest firmware, and try connecting directly to your cable modem to see if you still notice it resetting. My cable modem used to reset, and it was because of an issue with the lines which it sounds like Cox may have addressed. How are you certain the modem is resetting and not just your router ?