I have recently upgraded from win 8.1 to Win 10. Since the upgrade RDP wouldn't work correctly.
I couldn't use a recently used connection. Instead I had to open a new window each time. Today it stopped working completely.
If I tried to run mstsc.exe directly it would appear in task manager for less than a second before dissapearing.
Edit: Issue was traced to "custom scale factors" in display settings. See answer below.