email account

Depending on how  long ago the accounts were configured they were likely setup as POP account.  In this configuration email is not synchronized across different devices and whichever device happens to check your email at that given time will delete it from the server (webmail).  You could use the settings described at http://www.cox.com/residential/support/internet/article.cox?articleId=db0c9270-b1d9-11e2-d072-000000000000 which would cause emails going forward to sync across different devices.