Add $g_logo_image line to config/config_inc.php to use this new file.

What did you add to config_inc.php ?

The following (copied directly from config_inc.php):
$g_logo_image = 'images/axt-logo-232x80.png';

I assume there is more than one config_inc.php on your system and you did not change the right one.
To check it, add the following line to config_inc.php

die ("Hello from my config");

Do you see Hello from my config when refreshing the page?

There should only be one copy on the system.

I added the die('message'); to the end of config_inc.php and refreshed the page. The 'message' appears instead of the page.

In addition to this, mantisbt-2.5.1 is installed on two separate systems and both exhibit the same behaviour.

I assume we are talking about different things.
The image referenced by $g_logo_image is the one you see on top of the login page.
In older versions of Mantis, this one got also displayed on top of all other pages.

Maybe you are talking about the logo at the right bottom of the pages.
This one is not affected by changing $g_logo_image as it is part of the MantisBT branding.

Yep. Nailed it.
You are absolutely right. I was looking at the wrong image.