Constant service interuptions

We have been experiencing problems with our service (mostly with xbox live gaming) for many months.  We went to a service center and were told that we had a very old modem and needed an upgrade in order to get the faster speeds that our service should be getting.  We then purchased through Cox an all in one modem/router (Netgear AC1900/C6300BD) which they suggested.  Our speeds are way better now (117Mbps DS/12Mbps US and 12 ms latency) but our problems still exist.  The kids are constantly losing connection and having to restart while playing a game on xbox live.  They generally cannot play more than 30 min without having an error and often as little as every 5 min.  There is no difference in performance if the xbox is directly connected or connected through wifi.  They have even taken their xbox to a friends house and tested it on that Cox network.  They played for over an hour straight with no problems, leading us to believe that the xbox console is not the problem, rather something is wrong with our network.  I called the Tech support phone line, but that was no help.  Does anyone have any ideas what could be wrong and how we could fix it?