Originally Posted by anerbe
it could be the seating area on the wheel with corrosion or mis-seat that is causing a very small air loss.
This is what I would guess. That or the valve stem has a very small leak. It's unlikely the tire would have a puncture.
This has happened to me on multiple occasions and generally the low tire will hold air and just leak out very slowly. I had to fill my tire once every week or two before I made it in to Discount Tire and had them fix it.