This happens because MobileRead uses form-based authentication, which relies on cookies to work. The username/password that you can fill in applies to basic authentication, which works differently.
Right now the only way to access sites that use form-based authentication is to log in to the site through Mozilla or Firefox first, then point Sunrise to the browser's cookies.txt file. Sunrise will then send the required cookies, so you can access the site.
The next release will have dedicated support for
Form Logins. I just tested this with MobileRead and it works fine. The attached screenshot might make this all a little clearer.