can you add the following code to the login page after the body tag and to one of the problem pages after the body tag also:
<pre><?php var_dump($_SESSION); ?></pre>
this wil lwrite the session contents to the page.
also, what is the full url in the address bar when you get to the admin page, and what is the full URL in the address bar when you get directed back to the login page to re login? It important that I have the full URL including the domain