I've had an Azure Windows VM running on my free monthy credits for over a year now, to try stuff and play around in the cloud. I never had problems before.
For a few days now, I can't connect via rdp. It just doesn't work, although I'm sure I typed my password right on the 20th try.
So I tried to reset the password and configuration using Azure Portal. This always end in an error saying
"VMAccss extension does not work with domain controller"
I do know the VM is running, as I can access the website on it.
I restarted it a few times, and even redeployed it, but no dice.
What do I do now?
So Jason's solution was the one I used to solve my little access problem, so it is marked as such.
Azure changed over time though, so now there is an (IMO) actually better solution to this problem, posted by jmbertucci below.