I talked to the car people today, and was told, "We put in a new battery, and as for the tire, we can't find anything wrong with it."
I said doubtfully, "It was flat as a pancake." And she said emphatically, "I know! It's so weird!"
She said that they inspected the tire for damage and couldn't find any, took the tire off and did the dunk test (nothing), then put it back on and inflated it, and left it overnight and today, and it hadn't lost any air when I talked to her at two. It's the weirdest thing. While it wouldn't be surprising for it to have lost some air in this extreme cold, and sitting for ten days, it still shouldn't have been that flat without a leak. Perhaps some kids were messing around and let some air out? I mean, it's possible, though it seems unlikely.
Certainly I will keep a vigilant eye on it, and on the tire-pressure light, and bring it back at the first sign of trouble, but the bottom line is that, well, wouldn't they have wanted to sell me tires if they could? I think it's a good sign about them, actually. And I'm delighted to "only" have to pay for the battery today.
Plus, I got to get groceries! And while my younger self would have been rather disgusted to hear I was so pleased about that, well, it's nice to have some fresh food in the house.