I had a similar issue twice now. The first two times I talked to a support person, they did not know what was happening. After reaching a higher level of support, it was discovered that somehow my email accounts either had their passwords compromised, or were hacked. In the settings, someone had setup a forwarding email to a random gmail.com account, and it was set to delete the email after forwarding. I could still send email, but was not receiving any.
Log into your webmail account and check your settings. It might be a Settings item from the menu, or it might be a small gear icon, depending on which Cox email system you are on (they are upgrading it). Check your forwarding settings. It might not be the same issue, but it's worth checking. If you do find a forward, turn it off, change your password, and report it.
It would be nice if the system could notify me when the forwarding setting changed, but it cannot. It would also be nice if a device could be registered, or trusted, to access the webmail interface. I've scanned all my systems, have not installed any new apps, and never click any links from emails, but there is always the possibility that one of my devices or network somehow got compromised. The second tech support person I spoke with this evening (Martin I think) was very helpful and knowledgeable, but I am still not certain how this happened.