Infinite Loop With HTTP 401 Status?

I wrote an ASP.NET page that requires HTTP Basic authorization, which I put in the Page_Load function:

void Page_Load(object sender, EventArgs e)
{
string auth = Request.Headers["Authorization"];
if (string.IsNullOrEmpty(auth))
{
Response.StatusCode = 401;
}
else
{
string[] usernameAndPassword = Encoding.UTF8.GetString(Convert.FromBase64String(auth)).Split(':');
string username = usernameAndPassword[0];
string password = usernameAndPassword[1];
Login(username, password);
}
}

When I try to view the page in a browser (either Firefox or IE), it asks me for the username and password, and then...asks me for the username and password again.

Why does this happen, and how can I fix it?