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I spent time with the cox.net support representative and they couldn't solve this issue. I also spent time talking to Microsoft today (to solve an unrelated issue) and they helped me out with this one as well, but to no avail. No matter what I did, Outlook 365 will not connect to cox.net.
recommended cox.net settings for both IMAP and POP email. both don't work
Variations on all settings (SPA, ports, etc.), made no difference
using a brand-new Outlook profile. No change
using other email programs. In my case, I used Thunderbird to access the IMAP server with no problems, sending or receiving email.
verified password and connection to cox webmail. Check!
I'm honestly not sure at this point how to solve my problem. Am I just stuck with another email program? Lame.
Have you tried a different computer or a different network like cellular? Also, does it fail with a specific message?