Because whenever a forum link is clicked, you no longer load the rest of the page, and your browser doesn't care about intentions, only about what's sent to it in one specific request. To the browser, each new page has nothing to do with anything else.
You want something along the lines of
require 'header.php';
require 'navbar.php';
$pages = array('start.php', 'forum.php', 'forum_search.php', 'other_stuff.php');
if (!isset($pages[$_GET['page']])
$page = $pages[0];
else
$page = $pages[$_GET['page']];
require $page;
require 'footer.php';