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I do find that a call to customer service will get me all of my internet downtime credited back to me on my bill. I do this anytime my service is interrupted and have never been unable to get credit. I think it should be automatic, but at least it is done on request. Sometimes they will give you a full day credit for 10 or 12 hours of downtime. Can even be done over the internet chat customer service. 

If device is going up and down often look for the Cox cable technicians working in you area and ask them if any additional service outage complaints may help in getting whatever change/cable reolacement/reengeneering is needed for a beeter solution. Sometimes having the right local business customer complain or 10 to 30 of your fellow neighborhood residents can, by way of all actually making complaints and refund requests, get Cox to make more expensive changes or upgrades that will result in a better downtime VS uptime ratio for your service. 

As a former technician at the phone company, this was the best way to force their hand and likely the same will work forcing Cox. Personally I have never had more than 3 service outages in a year with Cox kver 20 years of service, and I would complain until this is all you see. 

If you have to, contact the public service commission and see if they can help.