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When I sign in to Cox, then click on Call History, a different sign in scrreen appears and I have to sign in again. When finished with the call history and trying to log off it doesn't work.
Create a shortcut to Call History and only sign in once. I can understand your annoyance, but with all the problems Cox has had with Call History, it's probably best if they leave it alone while it's working, even if it's not working exactly the way you prefer.
Call History: phonetools.cox.com/history
To completely sign out from Forums, you must "Sign out" and close your browser.
Webmail and Voice Tools are slightly different from Forums. If you have another browser tab open, clicking "Sign out" doesn't completely sign you out of Webmail or Voice Tools either. But, closing the browser requires re-authentication with your Cox credentials to access Webmail or Voice Tools again whether you signed out from your last session or just closed the browser.
The My Profile home page is more secure. Sign out requires re-authentication for access.
Update: Call History link address was updated to eliminate web page errors.