Hyundai: 95 Accent Mysterious problem

it's probably a near-dead battery and it couldn't take the energy of
turning on the brake lights and powering the brakes at once--if in your
words "shutting down" meant the engine just stalls.

~Scott

Yes by "shut down" I do mean stall.

I also forgot to mention, the car will most always start up right away
after the stall.

Thanks for your suggestion, I am looking into this. Has anyone else had
this problem?

jeh260 wrote: 

It could also be a vacuum problem; the brake booster servo
is vacuum-operated. Application of the brakes may be upsetting
the mixture enough (leakage?).

Speedy Jim
http://www.nls.net/mp/volks/

I can't recall whether this car has an idle switch. If so, check the
throttle position sensor and throttle cable for proper adjustment. Also
check the idle actuator. They've been known to stick now and then.