Cannot remote desktop into a machine after Windows 10 1903 update. Works first time then locks machine

It's a bug.
On 1903, force using the xddm driver for RDP via GPO and reboot.
Local Computer Policy - Computer Configuration - Administrative Templates - Windows Components - Remote Desktop Service - Remote Desktop Session Host - Remote Session Environment
-> Use WDDM graphics display driver for Remote Desktop Connections to DISABLED
This forces RDP to use the old (and now deprecated XDDM drivers)

There are at least two known bugs in 1903 that could cause his depending on what you are seeing.
Both are related to how Win 10 handles the graphics diver

The most likely match for your situation is that RDP does not cleanly log off the session leaving DWM.exe running and so effectively locking the session as open preventing a second concurrent session.

The workaround is to update graphics drivers if available and/or:
Force XDDM driver use via GPO
https://borncity.com/win/2019/08/28/windows-10-v1903-rdp-dwm-exe-causes-high-cpu-load-freezes-vms/

There is a second similar bug which results in the graphics adapter being ignored by RDP and a black screen appearing
https://mspoweruser.com/some-windows-10-may-2019-update-users-complaining-of-black-remote-desktop-screens/

See also
https://www.experts-exchange.com/posts/6030/RDP-Bug-in-Win10-v1903-disconnecting-RDP-sessions-WITHOUT.html

Thanks - but people seemed to have had some mixed results with these workarounds.

Does anyone have any idea if Microsoft have actually acknowledged this is an issue and/or are working on a fix ?

The second issue (Black screen when RDC to 1903 with older graphics) has been partially addressed by
https://support.microsoft.com/en-gb/help/4512941/windows-10-update-kb4512941

The XDDM issue (which seems most likely in your case) has not been publicly addressed as of posting today.

Results were not mixed here. It worked anywhere and all went back to normal.

https://answers.microsoft.com/en-us/windows/forum/windows_10-performance/after-exiting-a-remote-desktop-session-cpu-load/e21e7da0-9a64-4a14-a671-b7cb1b61f66e?messageId=2d647a47-eef9-4ac2-b806-11857ec2c1f1

That's what I say. They mention the same workaround.

And they say the results were mixed...…

Seems "results were mixed" because those applying them hadn't accurately identified the cause.

The XDDM fix is most appropriate where the graphics chipsets are no longer officially supported in Win 10 - as a result there's no incentive for Microsoft to address so if KB4512941 doesn't fix it it's currently your only other option short of replacing the older hardware.

No idea what graphics system you are dealing locally but if it fits this model then despite XDDM being deprecated is the only workaround.
Have you tested it as a solution yet?

It will need to be reapplied as future updates for the OS diverge further from this hardware as well.

There's no connection to graphic hardware as far as my experiences go. All were affected here, any (modern intel or Nvidia) hardware, even hyper-v VMs - and the xddm GPO helped anywhere.