Windows Mini PC?
If the audio device on Windows disappears, which I'm sure it would when you turn off the DAC, then of course MC can't play to it. It can't even see it anymore. If MC can't see it, it is going to stop playback. MC isn't going to start playback again just because you turn on the DAC and the audio device re-appears. In fact MC will switch to another available audio device when the one it is using disappears, I think. You could probably use Zoneswitch to have MC switch back to the DAC when you start playback again, though that would need to be tested, as a disappearing audio device may cause issues with that.
Nor is it going to keeping playing to a non-existent audio device while it isn't there, only to be heard again when you turn on the DAC. Is that really what you want, as you say? I guess maybe it would be useful if you were playing Radio Paradise or some other internet stream, but probably not if playing a Playlist and you own tracks.
The answer is to Stop playback before turning off the DAC, and then use a Remote such as Gizmo, JRemote for iOS, JRemote2 for Android, MO 4Media, etc. to restart playback on the DAC audio device when it appears again in MC. Again, Zoneswitch could be used to have MC switch to the DAC when playback starts.