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 (documented in chart); female patients (or female partners of male patients) must either be non-childbearing potential (hysterectomy, bilateral oophorectomy, bilateral tubal ligation or post-menopausal \> 1 year), or of childbearing potential and use 1 of the following highly effective methods of contraception (i.e., Pearl Index \< 1.0%) from 2 weeks prior to administration of study medication, throughout the study, and 28 days after completion or premature discontinuation from the study: * Complete abstinence from intercourse * Intrauterine device (IUD) * Two forms of barrier contraception (diaphragm plus spermicide, and for males condom plus spermicide) * Male partner is sterile prior to entry into the study and is the only partner of the female * Systemic contraceptives (combined or progesterone only) * Demonstrate the ability to swallow and retain oral medication * Patient or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure Exclusion Criteria: * Patients with a diagnosis of acute promyelocytic leukemia * Patients with a QTcF \> 450 msec (QTcF \> 480 msec for patients with Bundle Branch Block) * AML patients with persistent disease from the recent treatment defined as \> 5% blast and/or \> 20% cellularity and reported as persistent residual disease by a pathological report of the patient's bone marrow biopsy 14 days +/- 2 days from the initiation of cytarabine * Patients with known thrombophilic risk factors; exception: patients for whom the potential benefits of participating in the study outweigh the potential risks of thromboembolic events, as determined by the investigator * Current alcohol or drug abuse * Treatment with an investigational drug within 30 days or 5 half-lives (whichever is longer) preceding the first dose of study medication * Active and uncontrolled infections * Patients with known active hepatitis B, hepatitis C, or seropositive human immunodeficiency virus (HIV); testing is not required in the absence of clinical suspicion * Patients with liver cirrhosis (as determined by the investigator) * Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to eltrombopag or excipient that contraindicates the patients' participation * Patients of East Asian ancestry (i.e., Chinese, Japanese, Taiwanese, or Korean) * Patients with pre-existing cardiovascular disease (including congestive heart failure, New York Heart Association \[NYHA\] Grade III-IV), or arrhythmia known to increase the risk or thromboembolic events (e.g., atrial fibrillation) * Unwilling or unable to follow protocol requirements * Any condition which, in the Investigator's opinion, deems the patient an unsuitable candidate to receive study drug * No aspirin (ASA) or nonsteroidal antiinflammatory drugs (NSAIDS) administration