Vorinostat in Treating Patients With Recurrent or Persistent Ovarian Epithelial or Primary Peritoneal Cavity Cancer

Inclusion Criteria: * Histologically confirmed ovarian epithelial or primary peritoneal cavity cancer * Recurrent or persistent disease * Disease progression during OR persistent disease after completion of 1 prior platinum-based chemotherapy regimen (containing carboplatin, cisplatin, or other organoplatinum compound) for primary disease * Initial treatment may have included high-dose, consolidation, noncytotoxic agents, or extended therapy administered after surgical or non-surgical assessment * Treatment-free interval after completion of platinum-based chemotherapy must have been \< 12 months * Measurable disease, defined as ≥ 1 unidimensionally measurable target\* lesion ≥ 20 mm by conventional techniques (e.g., palpation, plain x-ray, CT scan, or MRI) OR ≥ 10 mm by spiral CT scan * Not eligible for a higher priority GOG protocol (i.e., any active phase III GOG protocol for the same patient population) * No known brain metastases * Performance status - GOG 0-1 * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * SGOT ≤ 2.5 times ULN * Alkaline phosphatase ≤ 2.5 times ULN * Creatinine ≤ 1.5 times ULN * No symptomatic congestive heart failure * No unstable angina pectoris * No cardiac arrhythmia * Able to take oral medication * No bowel obstruction * No persistent vomiting * No parenteral feeding * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for ≥ 1 month after completion of study treatment * No neuropathy (sensory and motor) \> grade 1 * No other invasive malignancy within the past 5 years except nonmelanoma skin cancer * No active infection requiring antibiotics * No psychiatric illness or social situation that would preclude study compliance * No history of allergic reaction attributed to compounds of similar chemical or biological composition to vorinostat * No other uncontrolled illness * At least 4 weeks since prior immunotherapy for the malignancy * At least 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) for the malignancy and recovered * No more than 2 prior cytotoxic chemotherapy regimens for recurrent or persistent disease * No prior non-cytotoxic chemotherapy for recurrent or persistent disease, unless therapy was part of the primary treatment regimen * No prior vorinostat * At least 1 week since prior hormonal therapy for the malignancy * Concurrent hormone replacement therapy allowed * At least 4 weeks since prior radiotherapy for the malignancy and recovered * No prior radiotherapy to \> 25% of bone marrow * At least 4 weeks since prior surgery for the malignancy and recovered * At least 4 weeks since other prior therapy for the malignancy * At least 30 days since prior and no concurrent valproic acid * Concurrent oral anticoagulants (i.e., warfarin) allowed provided there is increased vigilance with respect to monitoring PT/INR for the first 2 courses of study therapy or if there are any signs of bleeding * No prior anticancer therapy that would preclude study participation * No concurrent combination anti-retroviral therapy for HIV-positive patients * No other concurrent investigational agents