First, we have to look at what the doctor's second set of recommendations are. Those are to resume the initial dosage, but not to drink the beverage. When the patient complies, the patient still showed no change. This tells us why (E) is wrong: the medication might still be the wrong one. The patient's condition still hasn't improved on the doctor's medication, and so the possibility that the doctor prescribed the wrong medication is not ruled out.
(D), on the other hand, tells us the correct answer. The difference between the second set of recommendations and the original dosage was only the beverage, but even removing the beverage from the equation, nothing changed. Thus, if the prescribed dosage was ineffective, there had to be some other reason. Otherwise, if the patient's lack of healing was because of only the beverage, the patient's condition would have improved when he stopped drinking the beverage. Hope this helps!