You won't lose any audio quality from a cable box. Cable TV doesn't use the better audio codecs like you get with Blu-ray Disc or with some of the streaming services out there.
But, this screams cabling or Onkyo to me. For the most part, people seem to like their Onkyo receivers, but in my experience, their engineering is lackluster and a HDMI issue, possibly HDCP related, shouldn't be coming up ever, and if it does, should only take a few seconds to resolve itself. EDID is rather easy in the home market, and is often 1080i for cable boxes, but will include all supported resolutions such as 480i, 480p, 720p, 1080i, 1080p, and some 4K options for the newest gear.
It is certainly (and entirely!) possible that the cable box is causing the issue because cable box manufacturers are mostly worthless. So, you can do some searching around for the SPECIFIC model of your cable box to see if others are having a similar issue, but that would surprise me a bit if it is a known issue that hasn't been resolved or had a workaround figured out.