I have been having an issue with Gmail, as of late. It forgets the SMTP (send mail) password, then a week later the incoming password. I use two factor authentication and application passwords so resetting the passwords, while annoying only takes a minute or two.
All that by way of saying that you may be having a similar issue: Mail.app forgetting the password.
Change your email password then go into mail.app -> Preferences -> Accounts and change the Incoming Mail Server password. Then click on the Outgoing Mail Server (SMTP) drop down menu and select Edit SMTP server list. Click on the server for Cox and type in the new password there too. Click OK.
Now, BEFORE YOU CLOSE THE PREFERENCES WINDOW...
It seems that mail.app in Mavericks does not always save changes, when you change just the password. I have found that making a change to the Description (add a dash to the end of what you have there) will then prompt you to save when you close the preferences window.
If it DOESN'T ask you to save go back in and repeat the above and try changing another field (Description always works for me) and closing. You NEED to get the save dialog.
Now try to send some mail.
Failing that you may need to remove the mail preferences files from your ~/Library folder, there are at least a couple in different places. I will leave it to you to find them, delete them and re-add ALL your mail settings... sigh...
Best Answer
You can go directly to the folder where Mail saves its data through the Finder and duplicate it to store a copy elsewhere. Inside the Finder, menu Go > Go to Folder and then paste this path:
It is that V5 folder you'd want to back up before reseting Mail. There is also some software solutions like mailbackupx but I never used it so I can't say what it's worth.