My (2001) Hyundai XG300 keeps cutting out, once my gas is below 1/2 a tank, why?

First are you sure the fuel gauge is correct? If the tank is empty or close to it and the gauge reads 1/2, you simply have a gauge or sending unit problem - If you truly have 1/2 a tank of fuel when its acting up, it sounds like something is going on inside the fuel tank, such as the line coming off the fuel pump has a hole and is pushing/sucking air when the tank level goes down or the fuel pump is not sitting in its proper location and cannot pick up fuel when the level is lower.