sounds like an internaly leaking vacuum brake booster. you may or may not hear hissing whith the brakes applied. If you idle the car, then turn it off, you should still get 2 or more power assisted stops, for hours after turning off the engine. When restarting after pumping the pedal a few times, the pedal should sink under your foot as vacuum rebuilds in the booster(if it doesn't, the booster and/or its hose are dead. disconnect the booser hose at the check valve(you should only be able to blow through that one way), and plug the hose with a socket extension or bolt... Your braking effort will be much higher, but if it solves the stalling, you have located your problem.