Depsipeptide (Romidepsin) in Treating Patients With Recurrent Ovarian Epithelial or Peritoneal Cavity Cancer

Inclusion Criteria: * Histologically or cytologically confirmed primary ovarian epithelial or peritoneal cavity cancer * Histologic confirmation of recurrent disease not required * Measurable disease, defined as ≥ 1 unidimensionally measurable lesion ≥ 20 mm by conventional techniques (including palpation, plain x-ray, computed tomography \[CT\] scan, or magnetic resonance imaging \[MRI\]) OR ≥ 10 mm by spiral CT scan * Achieved a complete response after initial prior platinum-containing (cisplatin or carboplatin) chemotherapy regimen (e.g., conventional-dose therapy, high-dose therapy, consolidation therapy, or extended therapy after surgical or nonsurgical assessment) * Patients who have not received paclitaxel or docetaxel as initial therapy may receive a second regimen containing these drugs * No prior chemotherapy for persistent or recurrent disease, including re-treatment with the original regimen * Platinum-sensitive disease, defined as having a treatment-free interval with no evidence of progressive disease for \> 6 but \< 12 months after completion of a platinum-based regimen * No known brain metastases * Performance status - Eastern Cooperative Oncology Group (ECOG) 0-2 * Performance status - Karnofsky 60-100% * More than 6 months * White blood cells (WBC) ≥ 3,000/mm\^3 * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Bilirubin normal * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 times upper limit of normal (ULN) * Creatinine ≤ 1.5 times ULN * Creatinine clearance ≥ 60 mL/min * No New York Heart Association class III or IV congestive heart failure * No myocardial infarction within the past year * No uncontrolled dysrhythmias * No poorly controlled angina * No history of serious ventricular arrhythmia (e.g., ventricular tachycardia or ventricular fibrillation, ≥ 3 beats in a row) * QTc interval \< 500 msec * No other significant cardiac disease * Potassium normal * Magnesium normal * No uncontrolled electrolyte abnormality (hypokalemia and hypomagnesemia) * No ongoing or active infection requiring antibiotics * No history of allergic reactions attributed to compounds of similar chemical or biological composition to study drug * No neuropathy ≥ grade 2 * No other uncontrolled illness * No psychiatric illness or social situation that would preclude study compliance * No other invasive malignancy within the past 5 years except nonmelanoma skin cancer * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No prior monoclonal antibodies, cytokines, or signal transduction inhibitors for recurrent disease * No concurrent biologic therapy * See Disease Characteristics * More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) for the primary malignancy * No prior FR901228 (depsipeptide) * No other concurrent chemotherapy * More than 4 weeks since prior hormonal therapy for the primary malignancy * Concurrent estrogen replacement therapy allowed * More than 4 weeks since prior radiotherapy * No prior radiotherapy to \> 25% of bone marrow * No concurrent radiotherapy * Recovered from all prior therapy * More than 4 weeks since prior noncytotoxic therapy for the primary malignancy * No other prior noncytotoxic therapy for recurrent disease * No concurrent combination anti-retroviral therapy for HIV-positive patients * No other concurrent drugs known to have histone deacetylase inhibitor activity (e.g., valproic acid) * No concurrent agents that cause QTc prolongation * No other concurrent investigational agents * No other concurrent anticancer agents