Does it have a carburetor or fuel injection? If a carb and you give it throttle real slow does it still die? If not look at the accelerator pump in the carb.
Another possibility is the catalytic converter may be plugged. Easy check is get a vacuum gauge. and "T" it in to a vacuum line n the engine that pulls vacuum whenever the engine is running. slowly throttle up, and if the gauge jumps up then slowly drops off to nothing at the same time the engine slows down and dies .the engine is choked and you have a restriction in the exhaust
Have you checked the ignition system out? Sometimes bad ignition components can cause this problem. Change the spark plugs, wires, distributor cap, and rotary button. Also, check the carburetor's acceleration pump for operation. With the engine off, remove the air cleaner and look down the carburetor barrel. Quickly move the throttle lever from closed to fully open (or have a helper quickly push the accelerator pedal to the floor a few times). If the acceleration pump is working, you should see a stream of gas spray into the carburetor barrel.
Lets also not forget to check the fuel filter for clogs, and or dirty fuel, rule of thumb is to replace the fuel filter at 30-40,000 mile intervals, also is this vehicle carbureted or fuel injected, if injected its possible you have a bad fuel pressure relief valve problem(low rail pressure to the injectors) follow manufacturers repair/diagnostic procedures. Also if this happens only after the car is driven and warmed up a while, it is possible to have a clogged catalytic converter, consult a certified tech for testing procedures if you are not familiar with this diagnostic procedure.
Be certain you have a good gas cap on the tank as a poor /clogged gas cap vent can sometimes cause stalling on acceleration.
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