Here are questions that will help isolate the problem.
Is your client configured to use smtp over port 587 over TLS? Check your settings.
Has there been any change to your network's firewall?
Do you have a residential or commercial account?
Are you trying to connect out to a destined port 25 smtp server?
Cox refuses to let residential customers connect out to destined port 25 for residential customers. The only way the will allow it is to sign up for a more expensive, slower, commercial account. Just like they refuse to provide for the purchase of static IP's by residential users.
Do you have access to a telnet client or command shell on your Mac? if so, you can try to do this to see if you can connect or if you get a refused.
telnet smtp.mail.me.com 25 (this will probably fail with a connection rejected)
telnet smtp.mail.me.com 587 (this uses TLS and still may not work because the client won't have a cert, but you will still see a connection made)