The battery and charging system needs to be tested. It sounds to me that the alternator is not doing its job.
If the engine stalls and won't restart for several hours on a 2003 Santa Fe, there is a problem with the computer in the vehicle. Check to make sure all computer fuses are working properly.
The engine stalls and will not restart.
you have a sensor problem.
Replace the fuel pump. I had an S-10 that acted similarly - turned out it needed new spark plugs and wires.
the choke could be sticking causing the car the flood
Put shifter in park or neutral.
try this. under the driver's side front carpet is a ground connection. it is a black plastic connector about 3 inches long. the connection gets dirty and rusty from getting in with wet feet. hope this helps it did for me.
check your crank sensor
Its either your cam shaft position sensor or the crank sensor.
sounds like your ignition module
A major clue would be the vehicle stopping.
when kick down the gas pedal to accelerate, the car downshift but then stalls and then engine stays rough until i turn off the engine and restart it then the engine runs normal again till the next kick down.