If it doesn't indicate lost internet, then something else is causing the problem. IF it's happening on a wired system, run a ping test to google, 'ping -n 100 -4 www.google.com'
That will send/rec 100 packets using IPv4. If you get a string of dropped packets, it indicates an issue with either transmit or receive, and may indicate a tech is required. FIRST, swap the cable wire and the ethernet wire, and try again. If the results are the same, then yes, I would contact Cox and request a technician. IF the issue is indoor wiring, (coax through the walls, bad splitter, etc, ask about Cox Complete Care. it's 10$ a month, (I think), and covers the 75$ tech fee. Worth it I think.
If it happens to wireless and not wired. then it indicates emi or rf interference. Ensure the WiFi router is out in the open. NOT behind anything, NOT sitting on the floor, or in a smartbox, or in a cabinet. In the open, raised as high as it can be placed. The reason for raising it high, it wifi is a direct a-b-a signal, which means everything in between reduces the signal. The less things in between, the better the signal, the faster the wifi. A smartbox is stupid. think faraday cage.
Hope this helps, feel free to ask questions, I am actually a systems engineer, beta tested for several WiFi router companies, and actually hold a CNE, CCNE, A+, Network+, certs and/or training and advanced training in Bay Networks, Micom, Gandalf, Newbridge Mainstreet, Symplex, and more.