Even though the cookie record shows that I've got cookies from the NYTimes.com site, I am never recognized as a paid customer when visiting there, and must log in every time. This was not the case until a few days ago, when I had to reformat the hard drive and then reinstall the program with Win7 Home.
To check NYTimes.com's cookie permissions, right-click the page, choose View Page Info, then the Permissions tab. Is it set to "Allow" (either by default or explicitly)? This is necessary for the cookie to be saved with its standard expiration date.