The investigators hypothesis is that eltrombopag given to patients with moderate to very severe aplastic anemia will result in an increase in platelet counts. The investigators hypothesize that in patients with moderate to very severe aplastic anemia, treatment with eltrombopag will lead to fewer platelet transfusions, red blood cell transfusions, and fewer bleeding events. The investigators hypothesize that in patients with moderate to very severe aplastic anemia, eltrombopag will have an acceptable toxicity rate <3%, at doses that result in increased platelet counts. Finally the investigators hypothesize that plasma eltrombopag levels in peripheral blood will correlate with improved platelet counts.