It sounds like it could be a failing fuel pump.
As the fuel level gets lower, it has to work harder to pump the fuel to the engine bay.
Think of it this way. Lets say you were on a 5 story building and there was a bucket of water on the ground level. Imagine trying to suck the water up to your level thru a straw. Now imagine the bucket of water was 6" below your mouth. Much less effort is needed.