Thanks for suggestions.  There is no option in settings to skip POP. There used to be that option, but not now.  Another email app is a plan B.  I contacted Cox and was told they have been working with Apple, but it's been almost 2 weeks. I'll try Apple.  Maybe when they transition to Yahoo in our Northern Virginia area, that will provide a fix.

bemije wrote:

Maybe when they transition to Yahoo in our Northern Virginia area, that will provide a fix.

Could be. Someone else just posted a issue with webmail in VA.

They are lying. I used to beta test for apple and myself as well as a number of others reported this bug to apple YEARS ago. quick search shows over a million hits for search imap problems on iphone. 

About 1,260,000 results (0.39 seconds) 

Search Results

Why am I seeing an “IMAP server” error me…

Apple Support Community

https://discussions.apple.com › thread

May 11, 2021 — My iPhone has been displaying the error message "The IMAP server "imap.gmail.com is not responding. Check your network connection and that ...

I don't want to get into a finger pointing game but one way to test this is by trying another email provider like Gmail. If that does it too, it's a apple issue. If not, it could partly be a Cox issue. Either way I predict it will go away when Cox transitions to Yahoo which I think will be sometime this month.

Thanks for your info. I took a look at a few of the other discussions after searching per your comment, but most of them seem to have a different IMAP problem than what I'm experiencing.  I deleted my cox email account on the iphone, I deleted the mail app, I turned off the phone, I turned it on, reinstalled the mail app and tried to set up the cox.net email account. The phone doesn't even give me an option to set up IMAP. It automatically sets it up as POP.  I can get my gmail as IMAP and used to be able to get IMAP with cox.net, but for another reason that's separate from this issue, I deleted the mail app and that's when this particular problem occurred.  When I looked at some of the other search results, I found another one of yours where you recommended, "the FIX, is to delete the email ID off of the apple software on the phone, and then Re-Add it. then it will re-write the corrupted CFG file causing the issue, and it should start working again. "  Is that different than what I did re deleting the mail app and cox email account?  Is there something else I need to delete?  thanks

you have to install the email account manually instead of automatically. 

incoming=imap.cox.net/port 993/ssl

outgoing is smtp.cox.net/port 465/ssl

Just in case my issues can help other people, I will note that I can connect to a gmail email address I use, which is IMAP.  

When I use the "other" option to add my cox account email address and password, the iPhone automatically sets up a POP service as the next step. When I delete the pop.cox.net server name in the account settings and replace it with imap.cox.net along with the 993 port, I get an error that says "The POP server “imap.cox.net” is not responding. Check your network connection and that you entered the correct information in the “incoming mail server” field."  This is also happening on a new iPad we recently purchased.😟

bemije wrote:

I will note that I can connect to a gmail email address I use, which is IMAP

I don't think this is a server issue, but rather a configuration issue with the client(MacMail). It isn't detecting the IMAP server for some reason, even though the server functions. At least I assume it functions since I don't see others reporting the issue. Can you setup a new account with your gmail info? Does the IMAP option appear? Thank you for the follow up BTW.

I set up a second gmail email address without a problem.  With Google, the account must use IMAP by default because there were no options. The settings showed an IMAP connection.  Who is responsible for resolving a configuration issue as you described?  thanks