I have been having the exact same issue. This is not user error - there is absolutely something wrong with cox email delivery to some accounts. I work in IT for a large school district. I sent email from my work account to my personal cox account. Although the system at work received delivery confirmation, the email did NOT show up in my cox account for another 10 hours!!!
When I report this to Cox, I was told they have been migrating users to a new system. Apparently, the new system is misconfigured!!