Hello Dfsoa,
Do you see any alerts indicating what the issue may be in the Home app on your Mac mini when this happens? We ask because this could help us find a solution.
Next, have you tried restarting your HomePod to see if that resolves the issue for you? Follow these steps to do so:
Restart HomePod or HomePod mini
1. Open the Home app on your iPhone, iPad, or Mac that's signed in with the Apple ID that you used to set up HomePod.
2. Tap or click HomePod.
3. Scroll down, or tap or click the Settings icon
and scroll down.
4. If you have two HomePod speakers set up as a stereo pair, select Restart HomePod. If your HomePod speaker is not set up as a stereo pair, select Reset HomePod, then select Restart HomePod.
If you don't see an option to restart your HomePod, unplug it from power, then plug it back in and try again.
If HomePod still doesn't respond, reset it.
You'll find those steps here: If HomePod or HomePod mini isn't responding - Apple Support
Thanks!