If the problem(s) continue, could I convince you to buying your own router? IMO it's the way to go if you need advanced features. If you get the gateway for free, you could bridge it and use your own router. Or if you have phone service, you could swap it for a phone/data modem(eMTA) for free and use that with your own router. Finally, you could just buy your own seperate modem and router. I can give more advice depending on which way you want to go.
Thank you for the suggestion, but I was already aware of Bridge Mode on the Cox Gateway. I also have a router that I was using with the old Cox modem. I was in the process of trying to eliminate devices and cables, so I was glad to get a combination modem/router. Although the new gateway is ugly, it has the capability of doing everything I want. I just need them to fix this problem.
