There is no simple YES/NO answer to your question. It depends on how authentication is handled by the web site/server.
By default, http is STATELESS: each call into the server knows nothing about the previous call. In that case, you will have to authenticate EACH TIME you hit the server.
But most modern sites implement some kind of authentication persistence: either by maintaining user session information on the server, or, as Arnaud Bouchez mentioned, sending back a cookie that keeps track of your authentication.
I once wrote a custom web application that sent back an encrypted authentication token with the first response, and it was the client's (it was a custom Windows client with an embedded socket implemented using idhttp, not a browser client) responsibility to send back that token for each subsequent request.
So, your answer is: Let the server handle it - you generally don't have much choice.