This pilot clinical trial studies infusion of expanded cord blood hematopoietic progenitor cells following combination chemotherapy in treating younger patients with acute myeloid leukemia that has relapsed or has not responded to treatment. Chemotherapy drugs work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Chemotherapy also kills healthy infection-fighting cells, increasing the risk of infection. The infusion of expanded cord blood hematopoietic progenitor cells may be able to replace blood-forming cells that were destroyed by chemotherapy. This cellular therapy may decrease the risk of infection following chemotherapy.

Inclusion Criteria:

• Patients must have a diagnosis of AML or acute leukemia of ambiguous lineage according to World Health Organization (WHO) classification with >= 5% of disease in bone marrow (BM)

• Recipients of prior allogeneic hematopoietic stem cell transplantation for AML or acute leukemia of ambiguous lineage are eligible if they do not have graft-versus-host disease (GVHD) or they have quiescent GVHD whether or not they are receiving immunosuppressive therapy

• Must have a Lansky or Karnofsky performance status of >= 50; use Karnofsky for patients > 16 years of age and Lansky for patients =< 16 years of age

• Patients must have recovered from the acute toxicity of all prior chemotherapy

• The following amounts of time must have elapsed prior to entry on study:

  • 2 weeks from local radiation therapy (XRT)
  • 8 weeks from prior craniospinal or if > 50% of the pelvis has been irradiated
  • 6 weeks must have elapsed if other bone marrow radiation has occurred

• Adequate cardiac, renal, pulmonary, and hepatic function

• Patient must have a life expectancy of at least 2 months

• Females of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of treatment

• Females of childbearing potential and males should agree to use adequate contraception (barrier method of birth control) prior to study entry and for the duration of study participation

Exclusion Criteria:

• Recipients of prior allogeneic hematopoietic stem cell transplant (HSCT) with active acute or chronic GVHD
• Patients with history of Down's syndrome, Fanconi anemia or other known marrow failure condition
• Patients currently receiving other investigational drugs are not eligible
• Current concomitant chemotherapy, radiation therapy, or immunotherapy other than as specified in the protocol with the exception of intrathecal chemotherapy; this includes the tyrosine kinase inhibitor sorafenib which must not be initiated until patient demonstrates count recovery
• Patients with a systemic fungal, bacterial, viral, or other infection not controlled despite appropriate antibiotics or other treatment; uncontrolled systemic infections require infectious disease consultation for verification
• Patients who are platelet refractory prior to initiation of protocol therapy
• Pregnant or lactating patients
• Any significant concurrent disease, illness, or psychiatric disorder that would compromise patient safety or compliance, interfere with consent, study participation, follow up, or interpretation of study results