Cookies are being expired after application pool is recycled

I have an .NET 1.1 application running under an IIS 6.0.  This application makes use of  "Remember Me" option to save a persistant cookie so that the user doesn't need to login all the time.  This works completly fine and has been for many years on many differernt servers, but I just deployed this application to one client's computer and now, whenever the application pool recycles, the user's cookie isn't being used to log them in again, in essence, the cookie acts like it's expired or non-existent.  The IIS settings on this server and another server which works fine are completly the same and the web.config files are exactly the same.  I know the cookie still exists, and I can test that by closing my browser and going back to the site where I am logged back in automatically again using the cookie.  The only time that the cookie is not being accepted is if the application pool is recycled, even if I am in mid-session.  What would cause this one server to not accept valid cookies for logging in users after the session expires?  Any help is appreciated.