I'm not sure how to stop the DAC from shutting down when Mint goes to sleep, but maybe you can avoid the problem by making Mint not go to sleep in the first place? There's an option for it in the System Settings program, in the "power management" menu (under the "Hardware" heading).
Try doing that and see if the problem keeps happening. If it keeps happening, the DAC shutting down was probably caused by something else.
Small town in Oregon here (all measured along the routes walked, not 'as the crow flies'):
Now, I'm not entirely sure what separates a supermarket from a "big supermarket" in your mind, because to me all supermarkets are quite big by definition, so I'm going to explore three different trip options: one each to two supermarkets in or near my town, and one to the nearest Walmart, which I'm 100% sure should count as a "big supermarket", but which is a couple towns away.