It seems I've resolved the Windows issue: I had connected the AudioFuse Studio to the integrated USB 3 Hub of my BenQ PD3220U Monitor. After connecting it directly to the PC it looks like the audio output keeps working. No more restarting the AudioFuse every few minutes. Now I'm running the AudioFuse for multiple hours without interruption already :-)
Strangely this didn't happen with any other USB device or audio interface before.
But super happy it is working nicely now. :-)