I don't use Google Chrome or Cox webmail, so I may not be an authority. I didn't quite understand the statement "i over and over and over again clean history/cookies" but it could be a clue.
Do you try to protect your privacy by blocking sites and cookies? Meaning, within Chrome, you're opting to only allow cookies from specific sites or not allowing cookies from third-party sites? Check your Privacy and Security settings within Chrome and IE and tell us what you see.
Perhaps Cox can confirm this: did Cox change the URL to Cox webmail? If so and Rajaksin has an exception to only allow cookies from the previous URL, perhaps you just need to update the rule.
If there is no rule, it could be a problem with authentication. Sometimes, simply updating the date/time on your computer corrects a problem while other times updating your browser for the latest certificates. During boot, have you been getting messages from your BIOS about batteries? During timeouts, have you been getting little colored icon warnings near the URL about certificates?
Like the others have mentioned, it could be anything, but you need to be more observant of irregularities during your timeouts.