Cediranib Maleate in Treating Patients With Persistent, Recurrent, or Refractory Advanced Ovarian Epithelial, Peritoneal Cavity, or Fallopian Tube Cancer

Inclusion Criteria: Patients must have histologically or cytologically confirmed epithelial ovarian cancer, fallopian tube cancer, or primary peritoneal cancer that has recurred or is refractory to initial therapy; patients must have received platinum-based chemotherapy before entry into this protocol Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as > 20 mm with conventional techniques or as > 10 mm with spiral computed tomography (CT) scan OR patients must have evidence of progression based on an elevated CA-125 (defined as a value of > 2 x upper limit of normal [ULN] documented on two separate determinations made > 2 weeks apart) if the physical exam is normal and CT scan of the chest/abdomen/pelvis, has a disease volume < 1 cm in maximum diameter Patients may have received no more than one prior chemotherapy regimen (i.e. initial first-line chemotherapy only) Life expectancy of greater than 12 weeks Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%) Leukocytes >= 3,000/mcL Absolute neutrophil count >= 1,500/mcL Platelets >= 100,000/mcL Hemoglobin >= 8 g/dL Total bilirubin within normal institutional limits Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 × institutional upper limit of normal Creatinine within normal institutional limits OR creatinine clearance >= 60 mL/min/1.73 m^2 for patients with creatinine levels above institutional normal Women of child-bearing potential must have a negative pregnancy test prior to study entry; women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: Patients who have had chemotherapy, radiotherapy, or major surgery within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier Patients with borderline tumors or tumors of low malignant potential Patients with current bowel obstruction Patients may not be receiving any other investigational agents nor have participated in an investigational trial within the past 30 days Patients with known brain metastases should be excluded from this clinical trial History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD2171 (cediranib maleate) Mean corrected QT (QTc) > 470 msec (with Bazett's correction) in screening electrocardiogram or history of familial long QT syndrome Greater than +1 proteinuria on two consecutive dipsticks taken no less than 1 week apart Uncontrolled intercurrent illness including, but not limited to hypertension, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements Pregnant women are excluded from this study, breastfeeding should be discontinued if the mother is treated with AZD2171 Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible Any significant abnormality noted in the electrocardiogram (ECG) within 14 days of treatment A New York Heart Association classification of III or IV (NOTE: patients classified as class II controlled with treatment may continue with increase monitoring) Conditions requiring concurrent use of drugs or biologics with proarrythmic potential; these drugs are prohibited during studies with AZD2171