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This problem apparently was real but somewhat obscure. But, after two months of persistence with the Cox Digital team, the problem was solved.
In addition to the Server Error :: 3328 from the Contour App, we also started noticing timeout problems with specific web sites and certain email servers.
Finally, Cox sent out a tech who understood fiber, but (more importantly) was willing to take the problem seriously. While having us do some additional testing to eliminate the router, wifi, and modem (all while he stayed outside due to the pandemic), he was in contact with his supervisor, who in turn was in contact with higher-level techs/engineers. When he left our place after a couple of hours, he said they were pretty sure the problem had to so with some incorrect IP addressing/routing somewhere that was causing the timeout errors.
Well, about 24 hours later, my husband noticed all his email accounts started working (several gmail accounts would randomly not poll properly). I tried the web sites that had been problems and they all worked. Final test was the Contour app. Wow - it connected right up and has worked flawlessly ever since.
Not only that, about 45 minutes later we had a call from the service tech asking if the problem was fixed. We were pleased to tell him yes and give him a big thank you.
So, a huge round of applause and kudos to @JuanBonilla in Phoenix for helping us finally solve this annoying and long standing problem.
If you want to see more detail, search for 3328 in this forum (the initial post is now locked).