Ubuntu stops recognizing second display connected via KVM switch

I have a an Ubuntu tower and a Windows laptop. I have two displays, one of which is reserved for the tower, and one should be shared between the two devices via a 2 port KVM switch. The two devices also share keyboard and mouse.

This setup used to work well, until recently. I had changed the docking station for the laptop, but I can't imagine that this triggered the breakdown, since nothing happened on the tower-side of the KVM.

Now, if I boot Ubuntu while it's active in the KVM, both screens work. If I switch to the laptop and back, the shared display stays dark. I can still see it in the display settings.

I can activate the second screen as follows: If I change the display mode to mirrored, nothing changes. But if I "dont accept" the changes to the display mode, and it reverts to the original display mode, the second screen is recognized again.

My Ubuntu is Ubuntu 18.04.5 LTS. How can I proceed?

$ xrandr
Screen 0: minimum 320 x 200, current 3120 x 1920, maximum 16384 x 16384
DP-1 connected 1920x1200+1200+483 (normal left inverted right x axis y axis) 518mm x 324mm
   1920x1200     59.95*+
   1920x1080     60.00  
   1600x1200     60.00  
   1680x1050     59.95  
   1280x1024     60.02  
   1280x960      60.00  
   1024x768      60.00  
   800x600       60.32  
   640x480       59.94  
   720x400       70.08  
DP-2 connected primary 1200x1920+0+0 left (normal left inverted right x axis y axis) 518mm x 324mm
   1920x1200     59.95*+
   1920x1080     60.00  
   1600x1200     60.00  
   1680x1050     59.95  
   1280x1024     60.02  
   1280x960      60.00  
   1024x768      60.00  
   800x600       60.32  
   640x480       59.94  
   720x400       70.08  
DP-3 disconnected (normal left inverted right x axis y axis)
DP-4 disconnected (normal left inverted right x axis y axis)

Updating to 20.04 LTS did not help, but then installing proprietary nvidia drivers did solve the issue.