I found this problem requesting a site by C#
Here an interesting link
I also invite you to read the documentation that I am quoting here for you:
If the server sends HTTPOnly cookies, you should create a System.Net.CookieContainer on the request to hold the cookies, although you will not see or be able to access the cookies that are stored in the container. If you do not create a container to hold the cookies, the request will fail. For more information on HTTPOnly cookies, see HTTPOnly cookies..