The URL for any given test is permanent and the result is kept forever (within a reasonable definition of forever and assuming no disasters since there are no offsite backups). Anyone you give the URL to will be able to access the test. Even the “private” tests are available to everyone with the URL, they just use URLs that are not sequential or guessable (so it’s more privacy by obfuscation than any fancy scheme). Here is a test I just ran for another response here: http://www.webpagetest.org/result/130506_AF_J76/
The history itself doesn’t control access, it just makes the tests easier to find. You can keep the list on a sticky-note or in a spreadsheet if you want to make sure you don’t lose the URLs. If you are logged in when you run your tests then your history will follow your login as well and you won’t depend on the cookie.