First, the video dropouts. A couple times a day, your cable box will sync with the headend server(s) at Cox. While syncing...at least for me with the cable box directly connected to my TV...audio/video stops and a message appears on screen: "You're not subscribed to this channel [whatever channel]. To subscribe to this channel call (866) 961-0904." After the sync, my programming resumes. It's very annoying but I suppose essential.
I'd say your cable box isn't recovering after the sync, but you wrote it never happened while directly connected to your TV. It may be your Onkyo "thinking" you've turned off the cable box during the sync.
Does your Onkyo still have the cable box selected as its source after a sync? Do you have HDMI-CEC enabled? Onkyo calls HDMI-CEC RIHD (Remote Interactive over HDMI). If so, trying disabling it.
You could take your Onkyo out of the CATV loop by still directly connecting your cable box to the TV and then the TV to your Onkyo via HDMI-ARC or optical.