That's why you need to use a serious rust remover. There is probably a couple of inches of rusty mud at the bottom of your block and radiator. You keep stirring it up without getting all of it. A good power back flush would help too. That is where you use a compressed air flushing gun to force the muck backwards and out. Prestone used to sell a terrific 2-part cleaner. One side was the acid and the other was the neutralizer. Boy did that stuff work! There are others that work too. If you end up keeping the car, consider an acid flush and expect components to fail.