Eltrombopag Olamine in Treating Patients With Relapsed/Refractory Acute Myeloid Leukemia

Inclusion Criteria: * Relapsed/refractory AML patients who received standard of care cytarabine and mitoxantrone as their chemotherapy regimen * Patients must either have Grade 4 thrombocytopenia (platelet counts \< 25 x 10\^9/L) due to chemotherapy unless transfusion within 24-72 hours * Current systemic treatment for AML, with the exception of granulocyte colony-stimulating factor (G-CSF) must have been discontinued at least 7 days prior to entry into the study; in addition: * At least 4 weeks before Day 1 for interleukin (IL)-11 (oprelvekin) * At least 8 weeks before Day 1 for antithymocyte/antilymphocyte globulin * Patients with a prior stem cell transplant (SCT) must have failed the SCT * Patients must have documented hypoplasia from the bone marrow aspiration and biopsy 14 days +/- 2 days from the initiation of cytarabine treatment schedule (defined as \< 5% blasts and \< 20% cellularity) * Have an Eastern Cooperative Oncology Group (ECOG) Performance Status of =\< 2 * Patient is able to understand and comply with protocol requirements and instructions * Total bilirubin =\< 1.5 x upper limit of normal (ULN) except for Gilbert syndrome or cases clearly not indicative of inadequate organ function, i.e., elevation of indirect (hemolytic) bilirubin in the absence of alanine aminotransferase (ALT) and/or aspartate aminotransferase (AST) abnormality * ALT and AST =\< 3 x ULN * Creatinine =\< 1.5 x ULN * Patient is practicing an acceptable method of contraception (docume…