That reverse DNS check is usually used with connections involving TCP port 25 to submit mail; it’s a check of a peer mail server. That’s a spam-detection test. Most spam engines do not have valid DNS. Most computers running mail clients also do not have valid DNS, but do have authentication for the mail server; credentials
It’s fairly rare for a mail server to check a peer host when sending, but there are a few that are configured to do that. I’m going to,assume that’s not happening here, and that all addresses for sending mail that have been attempted here have failed.
Which means... More commonly...
If you’re configured and submitting mail to your mail server via TCP port 25, switch to submitting mail on TCP 465 or TCP 587; whichever port Cox supports/requires.
Also check... Mail clients have two sets of credentials and settings. These settings include the mail server host name and the mail server port and the user and password, as well as a security setting (TLS/SSL connection security, and that’s usually enabled in recent years), among other details. One set for sending via SMTP or ESMTP. Another set for receiving via POP or IMAP.
Mail clients will not send to the mail server when the credentials or settings for the mail server are INCORRECT.
Your settings for SMTP or ESMTP are INCORRECT, or Cox is having problems with their mail server. Most likely, the former.