Why would an h&h be low while in hospital with no history of anemia in a patient with aspiration pneumonia on continuous iv fluids?

See below: IV fluids may dilute the blood, especially if the person was dehydrated before entering the hospital and that would lower the H&H. Could the person be bleeding internally? Inflammation from pneumonia can suppress new blood formation. Finally repeated blood tests may contribute to developing anemia, by draining blood.

H & H: Hematocrit and hemoglobin could have dropped for any number of reasons.

Sounds normal: Modest anemia, i.e. low hematocrit and hemoglobin levels, almost always occurs along with serious infections like pneumonia, and with many other health problems. If the patient is otherwise healthy, the anemia should clear over a few weeks after the pneumonia has been treated. Discuss with the patient's doctor if you remain concerned about it.