Mike's XBox One is losing its Wi-Fi connection after about an hour. It won't even work with a hard wire. Leo says it could be a bad Wi-Fi radio, but that wouldn't have anything to do with the ethernet chip. There could be an issue with the DHCP host protocol. DHCP assigns IP addresses and they are dynamic, so they can expire.
Leo says it's a known issue on the XBox. If he Googles the issue, it comes up as a common problem. There's some suggestions on how to work around it. If he reboots the router and it fixes it, that will point to the issue. TomsHardware.com has an article about this issue here.