For several months now I’ve had a problem with my car stalling at random times, it starts back up after it’s been resting for about 30 minutes. It only seems to stall after I’ve been driving a while and when I hit the brakes. I’ve taken it to the mechanic twice and both times they couldn’t figure out the problem since the diagnostic computer was clueless and it wouldn’t stall during the test drive. Please give me any ideas you might have.
Intermittent problems are the hardest problems to diagnose. If the car won’t act up when a tech is trying to diagnose the problem it is almost impossible to determine the cause. If it doesn’t act up the tech can’t determine if it stalled because it lost spark or fuel it is critical to know this in determining what course of action to take.
The tech can guess as to what the problem is and start replacing parts which we call throwing parts at a problem. Throwing parts at a problem can be very expensive and frustrating for the customer.
Now I can speculate on the cause based on your brief description. It could be a ignition control module, a defective module can give you the type of problem you describe. As the module heats up it shuts down and the engine stalls, when it cools down the engine will restart.
I ran into an issue like this before, the vehicle would work fine idle fine never display a “code” went through modules etc… The I test drove the vehicle extended, upon pressing the brakes and coming up to a stop light or sign the vehicle would stall. The transmission lock up convertor solenoid was causing the issue, if this is something that is happening to you, you may need that switch and service, no you do not need a trans rebuild and the unit does not have to come out, its alittle difficult though. Try not to get inot a parts throwing contest, you will always lose.
have seen these cars have a problem with a leaking fuel pressure regulator. Just remove the vacuum hose for the regulator and see if it has fuel in it or that it smells like gas. The next time it stalls, instead of waiting 30 minutes press and hold gas pedal to floor. This is called the clear flood mode. If it is the reg it will start with pedal to floor.
it took me a week to find out what was wrong with mine chevy incorparated the oil pressure sending unit with the fuel pump relay (a good idea just not common). you can test this problem by disconnecting the plug going to the pressure switch (above coils) and jumping the the pink/black wire and gray wire together (use a paper clip or small wire) if it works first replace the sending unit ($8.50 o’rilleys auto) and reconnect if problem still exist oil pump is bad p.s. fuel pump will still work for prime but will shut off when car gets warm
There are several possibilities but I have one question. You state that it takes 30 minutes before it will restart.
After it dies have you attempted to restart the engine with the accelerator pedal depressed or are you leaving it as is?
This could make a difference in formulating an opinion, a.k.a. wild guess. 
Without knowing the above, you might consider:
Iffy Idle Air Valve if this only occurs at idle.
Power brake booster acting stupid.
Iffy fuel pump module.