The usual trigger is a mis-set SMTP server setting - whether the posted Cox support information is correct and matches the Cox SMTP servers is another discussion - or sometimes a problem where you're connecting to Cox on a network other than one in the Cox IP address space and are trying to access the Cox SMTP server via port 25. That port 25 access can work inside an ISP network, but can run afoul of spam filtering at the Cox SMTP servers when attempted remotely.
I've also seen a few cases where the local network or routing is messed up, but that tends to toss errors on attempts to access and receive messages, too; in the POP3 or IMAP path.
Also confirm your settings if this is effecting a reply, too, as I've seen a recent posting reporting an oddity here; I've not verified this misbehavior myself.
What to do? Work with someone that you can share your credentials with, verify the error, and (if it can't be resolved) contact Cox and explain to them how SMTP works.
And if the Cox SMTP servers are not working or not reliable, consider spending a few dollars a year and move to a mail provider with a mail server that you can operate with (and potentially manage). That migration has other advantages, too, such as allowing you to have your own domain, rather than depending on the potentially-volatile domain that an ISP such as Cox might choose or be using.
Don't know if you are still having cox mail problems buy I finally figured mine out and thought I would let you know what i did. You have to have your cox email and password entered under the outgoing mail server. go to your mail account thru preferences and click on the outoging server you have set up, this will bring up " edit server list " , then under advanced, and authentication ( which was set to none on my computer ) change the authentication to password. then you can enter your email address and password for your account and it should work. At least it did for me. Hope this helps