I was always told to run with a full tank. Reason ... sure its more weight ... but less liquid moving.
All of those hard turns push the liquids around and in a full tank they don't move as much.
But ... I have ran once or twice with a 1/2 a tank and haven't ran into those problems before ...
Might need to check your fuel pump or fuel filter. Might not be letting enough fuel go to the engine to at least have a few fumes of reserve before saying ... oh out of fuel.