Facebook losing logged in user with ajax - ajax

Question

I am writing a Facebook app and have used the Facebook php SDK so it can be authorized server side. I can see this is working because after authorization when Facebook redirects back to my app, I have the following code in my index.php...
require_once 'facebook.php';
$facebook = new Facebook(array(
'appId' => '111111111111111',
'secret' => '11111111111111111111111111111111',
'cookie' => true
));
// Get User ID
$user = $facebook->getUser();
...and $user returns not null. So far, so good!
I have a link on my app that loads content via ajax when clicked. Here's the JS:
$.post('my_content.php', {
action: 'render'
}, function(res){
if (res.html.length) {
$('.content').html(res.html);
}
},'json');
The problem is, the my_content.php script seems to be losing the fact the user has logged in and authorized the app.
The code I run in the my_content.php script to check whether the user is logged in is the same as in index.php
require_once 'facebook.php';
$facebook = new Facebook(array(
'appId' => '111111111111111',
'secret' => '11111111111111111111111111111111',
'cookie' => true
));
// Get User ID
$user = $facebook->getUser();
This time though $user = $facebook->getUser() returns null.
Is there a way to check if the user is logged in and authorized when running a PHP script with an AJAX call?
Should I store something in a session variable in my index.php script?
EDIT
After even more reading, I'm wondering if I need to retrieve the access token using the JavaScript SDK and pass it to my_content.php. Does anyone know if that's the correct way to do it?
EDIT 2
Turns out the line giving me the problem isn't $user = $facebook->getUser():
It is this one
$user_profile = $facebook->api('/me');
This line fails with the error 'OAuthException: An active access token must be used to query information about the current user.'
Strangely though, if I do this
$access_token = $facebook->getAccessToken();
$user = $facebook->getUser();
echo $access_token;
echo $user;
I do indeed have an access token and a user ID, so it looks like it may well be the bug reported by CBroe - check comments below.