Windows 7 rdp connection refused

Question

Several servers are connected in the same network at our office. Some run Windows 7, some Windows 10. We work on those machines from laptop computers connected either directly to the LAN or through VPN from outside by opening a Remote Desktop Connection.

This worked fine until about mid July 2019.

From then on RDP on the Windows 10 machines was still working fine. But when trying to connect to Windows 7 machines we had the following behavior:

1. The first connection (rdp session) was as expected.
2. After disconnecting rdp and re-connecting, the rdp window would show a Windows screen (probably loading the user profile), and lock in that state.
3. Re-trying to establish a rdp-session gives rdp error message "This computer can't connect to the remote computer. The two computers couldn't connect in the amount of time allotted. etc"
4. When re-booting a server, a first connection can again be started and the behavior is as stated above.

So I'm guessing the first rdp session was not properly disconnected, and is blocking new sessions. This behavior has changed with a Windows update around mid July 2019.

Any ideas on how to fix this?