i often check my email via the web. so i choose to leave a copy on the server
That's doesn't make sense. If you're using the "web" to check email...which assumes you're using Cox webmail...why would you need to leave a copy? You're not downloading it anywhere...you're just reading it on webmail.
Unless you're using another web client to check your email. If so, are those web clients configured as IMAP or POP?
It sounds like you're downloading the email somewhere...via POP...and just leaving an IMAP copy on the Cox server.
Either configure all your other clients as IMAP...or just use Cox webmail with the other devices...except your preferred-copy device.