Make http connection accessible in server busy mode

I want to access a site (third party, I do not have any server side access) via Httpwebrequest in c#. All works well but I want to access the site most at a certain time of the day, for 4-5 minutes. But this time the server flooded by user requests and server responds very slowly.

The time is almost fixed, that is when I want to get contents from it.And it gets inaccessible for that time due to loads of user hits.

Is there any technique, that can maximize my chance to get response from that site when it even gets busy? I search a lot but found nothing. If you could help me, I would be grateful. Thanks guys.

I'am Adding request and response header for your further understanding

Request Headers
--------------------
Connection:    keepalive
Accept-Encoding:    gzip,deflate
Accept:application/xml,application/xhtml+xml,text/html;q=0.9,text/plain;q=0.8,image/png,*/*;q=0.5
User-Agent:Mozilla/5.0 (Windows T 6.1) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/27.0.1453.116 Safari/537.36
Content-Type:application/x-www-form-urlencoded
Cookie: JSESSIONID=mWYJWy6TDfTLxJSTG8kWYgl1gLmjKvXrXQxFKwPcQTWgMSn1HlyH
Content-Length:652

Response Headers
-----------------
(Status-Line):    HTTP/1.1 200 OK
Cache-Control:    no-store
Content-Type:    text/html; charset=iso-8859-1
Server:    Microsoft-IIS/7.5
SET-COOKIE :JSESSIONID=mWYJWy6TDfTLxJSTG8kWYgl1gLmjKvXrXQxFKwPcQTWgMSn1HlyH
X-Powered-By: Servlet/2.5 JSP/2.1
Date:    Thu, 17 Dec 2015 04:30:44 GMT
Content-Length:    12467