That's a known issue unfortunately:
https://www.google.com/search?q=rdp+audio+stops+on+disconnectThe thing is, RDP creates a new desktop session when you connect (like a different user logging in), and the session is closed/paused when you disconnect - even if you don't log off, windows will release as many resources as it can from that temporary session.
You could try shadowing the Console session - ie, same desktop as the main logged in user - with this command (replace HOSTNAME):
mstsc /v:HOSTNAME /prompt /control /noConsentPrompt /shadow:1
This is not ideal though - the session number (1) may change, it always asks for credentials, and it's generally annoying. I much prefer to use RealVNC - you can setup a VNC desktop shortcut to connect directly to the target machine and it's seamless. Auto-scaling of the screen also works perfectly, which is tricky with RDP.