On the COX site they say they do not support IMAP.
Email Server Names for POP and SMTP
Last Updated: Thu, 04 Oct 2012 > Related Articles
Learn the Cox.net settings for POP and SMTP.
Before You Begin
These settings are for accessing your Cox.net email. For any other email service, you may need to enter a server name for both incoming and outgoing mail in order to get your cox.net email in your preferred email client.
Server Description POP or POP3 The Post Office Protocol (POP) is the incoming server. POP3 is POP version 3. You will either see POP or POP3 when configuring your email account(s). POP enables you to download messages from a the email host location to a computer. SMTP The Simple Mail Transfer Protocol (SMTP) is the outgoing server. It sends messages from your computer to the host.
Note: Cox does not currently support IMAP.
COX.net does work with IMAP
Heres how to configure cox.net as an IMAP account on your iOS device - http://ww2.cox.com/business/greaterlouisiana/support/data/article.cox?articleId= 8f807410-6c18-11e0-4e73-000000000000