Cisplatin and Flavopiridol in Treating Patients With Advanced Ovarian Epithelial Cancer or Primary Peritoneal Cancer

Inclusion Criteria:

* Histologically confirmed ovarian epithelial or primary peritoneal cancer:

Advanced disease

* Meets at least 1 of the following criteria:

  * Measurable disease;
  * Evaluable disease plus CA 125 \>= 2 times post-treatment nadir
* Treated with 1, and only 1, prior platin-containing chemotherapy regimen (e.g., paclitaxel or carboplatin-based) for ovarian epithelial or primary peritoneal cancer
* Prior treatment with the same regimen at first relapse allowed;

  * No more than 3 total chemotherapy regimens allowed provided exactly 1 has been platin-containing;
  * Must also have platin-resistant disease as defined for Group 1;
  * Rechallenge with a single regimen upon progression after a hiatus from therapy counts as a single regimen
* Group 1, meeting 1 of the following criteria:

  * Patients who relapse during or \< 6 months after completion of post-debulking chemotherapy;
  * "Platinum sensitive" patients in second relapse after having been treated/rechallenged with their initial regimen upon first relapse
* Group 2 (Closed to accrual as of 3/10/06):

  * Patients who relapse \>= 6 months after completion of post-debulking chemotherapy and are not retreated with the same or a different regimen
* No CNS metastases
* Performance status:

  * ECOG 0-2
* Hematopoietic:

  * Absolute neutrophil count \>= 1,500/mm3;
  * Platelet count \>= 100,000/mm3;
  * Hemoglobin \>= 10 g/dL (Note: May be supported with transfusion, epoetin alfa, or darbepoetin alfa)
* Hepatic:

  * AST =\< 2.5 times upper limit of normal (ULN);
  * Alkaline phosphatase =\< 2.5 times ULN;
  * Bilirubin =\< 1.5 times ULN
* Renal:

  * Creatinine =\< 1.5 times ULN
* Cardiovascular:

  * No cardiac arrhythmia;
  * No cardiac failure
* Not pregnant or nursing
* Negative pregnancy test
* More than 3 weeks since prior chemotherapy (6 weeks for nitrosoureas)
* More than 3 weeks since prior radiotherapy
* Recovered from all prior therapy
* Fertile patients must use effective contraception
* No other malignancy within the past 5 years except non-melanoma skin cancer or carcinoma in situ of the cervix
* No diabetes
* No peripheral neuropathy \>= grade 2
* No baseline diarrhea (\>= 4 stools/day)
* No uncontrolled infection
* No other concurrent uncontrolled serious medical condition
* No concurrent routine colony-stimulating factors