how to maintain a session through out a browser until it closes with out any login form

In my view if you just want to avoid authentication on session timeout you can opt for maintaining SessionID in Application Context once successfully authenticated.

STEP 1:
After successful authentication keep the current SessionID and UserId in the Application State.
Also keep the UserID in the current session.

STEP 2:
On page load
If UserID exists in current session then go ahead.
Else check if the Request SessionID(you could determine from HttpContext.Current.Request.Cookies["ASP.NET_SessionId"].Value) exists in your Application State.
{
If exists then store the UserID in current session and go ahead.
Else user hits first time, so redirect to logon page.
}

STEP 3:
Expire the user session on following events;
1. Logout by user
2. Catch the browser close event from JavaScript and notify the server to close the session.

Other points to note:
1. You must understand that, you should not use the session variable in this scenario.
2. Use following configuration to avoid generate same SessionId again, and avoid conflicting with other user session.
<configuration>
<system.web>
regenerateExpiredSessionId="false" />


3. Still there could be some live SessionID in your Application state, which actually does not exists as browser crashed or something unusual happened. So need to clean those periodically.