What causes a car to want to die sitting still?

When a car won't start or stalls, there is one of three core problems typically:

1) Spark, ignition, electrical

2) Fuel, delivery, mix, supply (mix includes air)

3) Compression

You need fuel into the cylinders, you need a spark to ignite the fuel air mixture and you need compression to capture the energy released when the fuel air mixture ignites.

When trouble shooting a problem you should move from easy to hard.

Are the spark plugs gapped right, not worn and clean? Are the spark plug wires free of cracks on the insulation and not worn? Is the battery holding a charge? Is the voltage regulator operating properly? Does the ECM module need an update from the factory (is there a TSB on stalling)

Is the fuel injection pressure running normally? Is the air filter clean? Is the fuel filter clean? Are you using the right gas? Is the throttle cable, and idle settings correct? Is the emission system operating properly including having the proper catalytic converter in place and the right amount of back pressure to support proper ignition.

Do the cylinders pass a compression test? Is the head gasket leaking? Is the head gasket failed? Are the valves seating properly? Are the heads cracked?

Long list, but if you start simple (air filter, plugs, wires, etc etc.) you may self-diagnosis and save a lot of money.