• Patient must have histologically or cytologically documented evidence of prostate adenocarcinoma

• Patient must previously have undergone radical prostatectomy

• Patient must previously have undergone either adjuvant or salvage radiation therapy to the prostatic fossa +/- whole pelvis

• Patient must have a prostate specific antigen (PSA) \>= 0.2 and \< 10 ng/mL. If there is only one PSA value that has risen to \>= 0.2 with this biochemical recurrence, a second PSA value must be confirmed to be within \>= 0.2 and \< 10 ng/mL at least 2 weeks from the first value and within 28 days of enrollment

• PSA doubling time must be calculated utilizing either all PSA measurements \> 0.1 ng/mL from most recent biochemically-recurred (BCR) or the most recent 3 PSA measurements \> 0.1 ng/mL (if the latter, all 3 PSA measurements must be \> 2 weeks apart to be used in the calculation). PSA doubling time must be \> 3 months and \< 18 months. The Memorial Sloan Kettering PSA doubling time calculator should be used

• Patient must have no previous evidence of radiographically detectable metastatic prostate cancer by conventional CT and bone scan imaging

• Patient must have total testosterone level \> 120 ng/dL demonstrated within 42 days of enrollment

• Patient must have Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

• Absolute neutrophil count (ANC) \>= 1.0 X 10\^9/L

• Platelet count \>= 100 X 10\^9/L

• Hemoglobin \>= 9 g/dL

• Potassium \>= 3.5

• Serum bilirubin =\< 1.5 X upper limit of normal (ULN) or =\< 3 X ULN for patients with documented Gilbert's syndrome

• Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 X ULN

• Creatinine clearance (Cr Cl) \>= 30 mL/min as estimated by the Cockcroft-Gault criteria or as determined by 24 hour Cr Cl measurement

• Patient must be \>= 18 years of age on day of signing informed consent

• Patient must be able to understand and authorize informed consent