It is iron they test for, not hemoglobin. They only take a pint of blood from you - that's 2 cups, not three.

And every woman's body is different, some women lose a lot of iron around their menstrual cycle, others it has little to no effect. A lot depends on your diet, I for example, cannot eat most red meat because of allergies, so I have to stay healthy by making sure I get enough iron other ways.