I don't know about you, but for some reason, you can bash your head for 2 days on a problem. Finally decide to ask for help and insights. And the moment you hit "sent", you find the solution to your problem.
I'm still running some more tests, but it seems to have been the firewall which caused the problems. The firewall is running host-headers to share 1 IP with serveral URL's. And that is where it was failing.
I managed to free up an IP for mattermost, and for now it seems to be updating the direct messages as expected.
I will run some more testing to see if it really fixed the problem.