How to use Yosemite Apple Mail with Cox Webmail

I have been using Apple Mail to manage Cox web mail since February 2011 when I bought my first MacBook. On December 1, 2015, I started getting messages that Mail cannot connect to the Cox server. I don't know what changed on that day. A couple of weeks later, my husband started getting the same messages on his MacBook. The error messages display when I try to send mail, receive mail, or run Connection Doctor. The same thing happens no matter which network I am connected to. I have found the documents on Cox site that show how to set up the connection, and have rechecked them a hundred times. I have tried to set up a new Cox account with a different name, I have tried both POP and IMAP accounts. I can get my email from the Cox webmail site, so that proves that the account itself is active and my login ID and password are valid. I can get email from Yahoo and Google and Apple iCloud accounts.

My Internet search turns up lots of people complaining about this problem with Apple and Cox a couple of years ago, but the only solution (besides the same thing that Cox publishes on their site) is to use a different mail client (e.g., Thunderbird). I have already called Cox, and they don't seem to have a clue what happened. Has anyone had this problem with Yosemite and have ideas how to resolve it?