Flavopiridol, Cytarabine, and Mitoxantrone in Treating Patients With Relapsed or Refractory Acute Leukemia

Inclusion Criteria: * Pathologically confirmed acute myeloid leukemia or acute lymphoblastic leukemia: * Relapsed \>= 1 time OR refractory disease: * Patients who fail primary induction therapy or who relapse after achieving complete remission are eligible if they have received =\< 3 prior courses of induction/reinduction therapy * Relapsed \>= 1 time OR refractory disease * Patients who fail primary induction therapy or who relapse after achieving complete remission are eligible if they have received =\< 3 prior courses of induction/reinduction therapy * No active CNS leukemia * ECOG performance status 0-2 * AST and ALT =\< 5 times upper limit normal (ULN) * Alkaline phosphatase =\< 5 times ULN * Bilirubin =\< 2.0 mg/dL * Creatinine =\< 2.0 mg/dL * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * LVEF \>= 45% by MUGA or ECHO * No active, uncontrolled infection * No other life-threatening illness * No mental deficits and/or psychiatric history that would preclude study compliance * No active graft-vs-host disease * Recovered from all prior therapies * At least 24 hours since prior hydroxyurea, steroids, imatinib mesylate, arsenic trioxide, interferon, or leukapheresis for blast count control * At least 4 weeks since prior stem cell transplantation (autologous or allogeneic) * At least 4 days since prior growth factors * At least 3 weeks since prior chemotherapy, except for non-aplasia producing treatments (e.g., low-dose cyclophosphamide, hydroxyurea, interferon, imatinib mesylate, mercaptopurine, thalidomide, azacitidine, or decitabine) * No prior flavopiridol * No other concurrent chemotherapy, radiotherapy, or immunotherapy * No acute promyelocytic leukemia (M3) * No hyperleukocytosis with \> 50,000 blasts/mm\^3