Breaking out from another post:
I have a few different user IDs for different purposes (hobby forums, important stuff, etc) When I view Webmail (Firefox, Win7) I used to be able to sign out using ...
I use Chrome and clicking "Sign out" in the Settings menu takes me to the "Sign in to Webmail" page. So, it doesn't appear to be an issue with Chrome.
Delete "myemail.cox.net" cookies
From the Cox Webmail page, click the "View site information" icon.(upper left just to the left of the Omnibox)
Click "Site settings"
"Usage" may display "No usage data" initially. Wait for the number of cookies to display (may take 30-60 seconds). Then click "Clear data" to delete only "myemail.cox.net" cookies.
Check for bad extensions
While in Site settings, click "Safety check". Then click the "Check now" button. This may remove extensions that you've added (good or bad). So, just be aware.
Or, at the top right, click MoretoolsExtensions to eliminate other variables while testing each enabled extension.