You've got a bad vacuum element,

This is common. The driver's door has a switch. Other 3 doors, gas door, and trunk have elements. Since you have the door panels out(I ussually diagnois by removing carpets ), listen to each door when the lock is up. I'm assuming the engine will not kill in this mode either? Correct.
If you can hear the leak in a door-then replace the element- about $30. Most people test them with a little mightyvac hand pump(can buy them at Sears or elsewhere).

I expect 6-12 years is reasonable for these components. Best luck,

Michael

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Michael McGuire
83 300d
01 vw A4 TDI
66 Chevy Corsa
68 GMC V6 w/oD
86 300E