Favicon missing in admin menu when viewing site via proxy server

Situation:

Suppose the Drupal site has location:
http://gkrshow.dk/drupal

Site is enabled for access via a secure proxy server:
https://relay.ditonlinebetalingssystem.dk/relay/v2/relay.cgi/gkrshow.dk/drupal

In order that (among other things) all the href attributes in <link> elements for stylesheets are adjusted to the correct path for viewing through the proxy I have added this in settings.php:

if ($_SERVER['REMOTE_ADDR'] == '80.62.243.167') {
  $base_url = 'https://relay.ditonlinebetalingssystem.dk/relay/v2/relay.cgi/gkrshow.dk/drupal';
}

Method is described here:
http://drupal.org/node/339552

Problem:

The favicon in the admin menu does not show when I view the page via the proxy.

Screen shot, no proxy (favicon in admin menu is fine):
http://img10.imageshack.us/img10/9541/ss20091119171750.png

Screen shot, via secure proxy (favicon missing in admin menu):
http://img10.imageshack.us/img10/2713/ss200911191718312.png

When I look in the HTML I see a wrong path to the image (see Firebug in last screen shot):

src="/drupal/misc/favicon.ico"

When it should have been

src="/relay/v2/relay.cgi/gkrshow.dk/drupal/misc/favicon.ico"

For some reason the src attribute for the favicon image in the admin menu is not adjusted according to the specified $base_url. All other links on the page are working correctly. Only the favicon in the admin menu has broken link.

I have tried for several hours to locate the error, but I started getting head ache. Somewhere admin_menu must be forgetting to adjust the src attribute for the menu favicon, but I am not sure where and how this should happen.