My car cuts out when on quarter tank or lower of fuel. Why is that?

My guess is the fuel gauge may be reading inaccurately most likely a defective fuel tank sender unit. If this is not the problem, the problem may be the pick up in the fuel tank.

I know what it means to run the car on as little gas as you can. Understand something, the gas is what lubricates the fuel pump. It is a 18 year old car. if you have done the practice of running the fuel level that low on a regular basis you most likely have a bad fuel pump. Someone needs to perform a fuel pressure and volume test on the fuel system.