My 2006 mustang runs the shuts down?
Wow, there's a lot that this could be.
If at all possible, you need to get the codes read on the car. If you can get it to autozone, you can usually get the codes read for free. The codes might indicate a sensor problem.
One potential is that you could have a bad fuel filter. This will cause limited the engine to run poorly at anything over an idle, or worse. You could also have a bad fuel pump. There are way to check for this, if you "know what you are doing".