I have an application that performs click on screen that's running on Windows 2019 Server instance
but the thing is that when I close RDP, then application stops working (clicking)
I suspect that this is caused by User logging out when I close RDP (using "X" button).
Is there any way to "don't lose screen" when I close RDP?
by using the "X" button on your RDP session you do not get logged off. You will be disconnected and your user session is still there. Anyway there is a Windows-GPO that can be used to set a time limit on disconnected sessions.
Computer Configuration/Administrative Templates/Windows Components/Remote Desktop Services/Remote Desktop Session Host/Session Time Limits
There should be a setting Set time limit for disconnected sessions. Check if it is Not Configured or Enabled with Never.
If this does not solve your Problem it is probably a problem with the application that needs a connected User Session.
Greetings.