Engine stalls?

1987 Nissan Stanza Wagon mileage: 104,000. Hello, I've read through the previous letters on stalling, but here's mine. Starts and runs fine in morning, but stalls after parking more than 10 minutes, it runs for 15 seconds, shuts off, starts for 3 seconds, shuts off. Will not start until I can hear a “Hum” instead of a “Whine” by turning key to “On.” Fuel pump has been replaced twice. Had suggestion it may be related to alternator, which was marginal, but no change after a new one.