Unfortunately, its rather worse than you would have hoped to see. This issue seems to have been first reported on Jul 16 2011 within the developers forum. The developer came into the forum and replied a few times, stating that adverts were working for him.
At the time they may have been, but it seems that later, a wordpress update caused the adverts to break.
The last reply from the developer was on Jul 17 2011.
You can view the thread here: https://cartpauj.icomnow.com/forum/mingle-forum-plugin-group1/support-forum6/google-adsense-ad-not-showing-thread1709.0/
Having read the thread (and most of the forum) and having seen the same thing happen over and over again with free plugins, I honestly wonder why we continue to rely on free plugins. So many times, developers of great open source plugins abandon their projects because it is taking up too much of their time and money to be able to develop the plugin and provide any level of support.
This leaves many people who are using the plugin with no support. In the case of Mingle Forum, there have been at least 180,862 downloads.
If you check the developers profile on WordPress, the last reply that they made to a thread was 141 days ago! The last update that they made to the plugin on WordPress was 64 days ago. If they updated the plugin just 64 days ago, it makes you wonder why they have not replied to recent posts within their forum that are more than 64 days old. I guess that they just do not have the time.