You have to weigh your options. Do you want Cox to track your browsing history...collect your online activity...and fill your browser with behaviorally-targeted ads? Yes? Then don't automatically delete your history on exit.
Every time my browser has the wrong city, it confirms Cox can't track me. Ha-ha, you!
Deleting the history/cookies on exit is what is causing you to have to re-enter your zip code each time. You can set your browser to delete on exit, or delete when you choose. Anytime that the cookies are deleted, the site will need you to enter your location.