Is this a battery problem?

[Kurt in NJ]

what happens if you go for a 3 mile drive, leave the car parked in the driveway for the same amount of time you shop?

Give more of a description of your electrical system ---generator, alternator, 6V, 12V

When you come out and try to start it does it crank slow, or is it seemingly totally dead?

When you park at home do you leave it on a charger (a battery maintainer charger?)

Have you tried different shopping centers, maybe the car doesn't like the one you go to.