The body is destroying the red blood cells at too high a rate. With her taking three doses a day for six weeks, the most common way she could have had that lack of absorption is if the dose was incorrect or your daughter was drinking a lot of cow's milk. Her anemia is caused by something else. This ought to be investigated because if her anemia is not from iron deficiency, then she certainly doesn't require iron supplementation. And in fact, prolonged iron supplementation when it isn't needed can cause problems with iron overload later in life.
Many states require as part of their newborn screen a test called a hemoglobin electrophoresis.
This test looks for inherited causes of anemia. I suggest you find out if your daughter had this screen. If she did not have this screen or it does not supply the answer to the anemia, I would suggest getting a second opinion. The cause of anemia can usually be determined, and it is important to figure it out. If she is truly iron deficient, supplying the correct amount of iron to her body is critical for her behavioral and cognitive development.