Car dies after starting

I have a problem with my ?84 Cad Seville. Ther car still runs fine, pretty good gas mileage, very comfortable ride but…sometimes she refuses to start. Here?s what happens:

When I start out on some errands and get to my first stop, park and go in the store or whatever, come out turn on the ignition she fires right up and then dies. She makes me wait a while, sometimes five minutes or more, and then starts up, sometimes a little accelerator action is required. There is never a gasoline smell and I think it might be in the fuel feed but I have had it to a Cad shop three times now and they cannot find the problem.