Vaccine Therapy in Treating Patients With Recurrent Prostate Cancer

Inclusion Criteria: * Histologically confirmed adenocarcinoma of the prostate * Must have undergone radical prostatectomy ≥ 3 months ago * Prostate-specific antigen (PSA) level ≥ 0.6 ng/mL and rising (after radical prostatectomy) on ≥ 2 measurements separated by ≥ 3 months * HLA-A2-positive peripheral blood mononuclear cells by flow cytometry * No clinical evidence of local recurrence * No palpable induration or mass in prostatic fossa * No metastatic prostate cancer * No osseous metastases by bone scan * Performance status - ECOG 0-1 * Performance status - Karnofsky 70-100% * More than 1 year * WBC ≥ 3,000/mm\^3 * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * AST and ALT ≤ 2.5 times upper limit of normal * Bilirubin normal * Hepatitis B and C negative * Creatinine normal * Creatinine clearance ≥ 60 mL/min * No symptomatic congestive heart failure * No unstable angina pectoris * No cardiac arrhythmia * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to study PSA peptide vaccine or Montanide ISA-51 * No history of systemic autoimmune disease or autoimmune disease requiring anti-inflammatory or immunosuppressive therapy * Patients with history of autoimmune thyroiditis are eligible provided the patient requires only thyroid hormone replacement therapy AND disease has been stable for ≥ 1 year * No known HIV positivity * No ongoing or active infection * No primary or secondary immune deficiency * No psychiatric illness or social situation that would preclude study compliance * No history of other uncontrolled illness * No prior chemotherapy * No prior hormonal therapy * No concurrent systemic or ocular steroid therapy, except for any of the following: * Inhaled steroids for asthma * Limited topical steroids * Replacement doses of cortisone * More than 4 weeks since prior radiotherapy * No prior radiotherapy to the prostate * Prior radiotherapy to the pelvis after radical prostatectomy allowed * See Disease Characteristics * No other concurrent investigational agents * No other concurrent anticancer therapy