What modem are you using? What are the indicators lights on the modem doing when your speed drops?
If it's an issue with cox Equipment or delivery of service to your home, it will be fixed/replaced for free, if it's wiring from the audit box to the inside of your home, if you do not have Cox Complete Care, there may be a service charge for repairs.
That being said, Cox tier 1 support is no longer technically trained, and don't have a clue. All they have is a monkey script called Solution Center which is about as useful as a 20 year old coon dog with bad breath and a kerosine A$$. Think, north end of a south bound mule. The next step up, CAG, is technically trained and they would be the people I would ask for if the problem isn't fixed by the tech.
Customer surveys are random.