Ongoing imap server issues...

Outlook 2016 and Mozilla Thunderbird intermittently (10-20 times per day) telling me that it cannot log in to imap.cox.net and ask me to verify my credentials. We experience this on 4 different computers for several months now. The credentials are fine. If I wait, the client will eventually connect. The same credentials also log me into www.cox.net email.  The problem is that I have app up box that pops up 10-20 times per day.   I tried resetting my password, recreating my profile, reinstalling outlook, shutting down antivirus and firewall programs, nothing resolves this.

Juan from "CAG level Support" says Cox does not support 3rd party email applications and provides no way to escalate this problem. Cox refuses to trouble shoot their end of the email server, even though the service apparently admitted there was an outage on their imap server last week and they advertise how to use imap and pop accounts with Cox service.  This is maddening as I am paying $$$ bucks per month for Cox internet and TV service.