Your image has been cached after the first request and all other requests will try to get the file from the cache first and if the file has been found - no requests to the internet will be made.
If you want to avoid it:
1) At your own server with files you can modify Cache-Control: max-age
header value to some time when image can be cached.
2) Build unique request URI for the each request like client.OpenReadAsync(new Uri(@"http://www.myurl.com/" + path + "/" + number.ToString() + ".jpg" + "?rand=" + GetRandomNumber()), client);