Changing expiry on ASP.NET's Session State cookie

I'm using ASP.NET Session State to keep track of logged in users on my site.

However, one problem I'm running into is that by default ASP.NET session cookies are set to expire when the browser closes.

http://ahb.me/43e

I've tried setting my own ASP.NET_SessionId cookie and modifying the cookie's expiry using something similar to the following code:

Response.Cookies["ASP.NET_SessionId"].Expires = DateTime.Now.AddMonths(1);

None of these approaches work, they all set a second cookie with the same name.

Is there a way of changing the session cookie's expiry?