Darn, a gateway. They don't have event logs as far as I know but you can look up signal levels at 192.168.0.1 >login > Connection > Cox Network. The UI is hard to copy/paste. Main thing you want to look for is your downstream is +5 to -5dB with SNR above 35/36. Upstream should be below 50dB.
Also, do you lose phone service when you lose data service?
Nothing you can change in the UI of the gateway, but it might tell you the nature of the problem. It's probably T3 errors on the upstream, but since the gateways don't keep logs, there is know way to confirm it. I am hoping the signal levels show something else obvious that might lead to a work around.
Also, can you explain how the coaxial gets from the street to the room the modem is in? Any splitters/amps? Even though you are data only, sometimes there can be outlets left over from when the house had TV service.