Gene Therapy and Radioactive Iodine in Treating Patients With Locally Recurrent Prostate Cancer That Did Not Respond to Radiation Therapy

DISEASE CHARACTERISTICS: * Histologically confirmed recurrent adenocarcinoma of the prostate within the past year * No transitional cell, small cell, or squamous cell carcinoma of the prostate * Local recurrence * Disease recurred ≥ 18 months after completion of prior external beam radiotherapy or brachytherapy for stage T1-T3, N0/X, M0 disease * Biochemical failure as defined by the Phoenix definition (rise in PSA by 2 ng/mL or more above the nadir PSA) * PSA ≥ 0.3 ng/mL to \< 20 ng/mL measured within the past 30 days * Pre-treatment PSA \< 50 ng/mL * Prior locally recurrent hormone-refractory disease allowed * American Urologic Association Obstructive Symptom Index Score ≤ 24 * No known standard therapy that is potentially curative or definitely capable of extending life expectancy * No evidence of or history of metastatic adenocarcinoma of the prostate * Negative radiographic metastatic work-up including whole-body radionuclide bone scan, CT and/or MR scan of the pelvis and abdomen, and chest x-ray * Patients with suspicious areas on conventional imaging studies are eligible provided they are biopsy negative * No known CNS metastases * No prostate size \> 140 cc PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Life expectancy ≥ 12 weeks * ANC ≥ 1,500/μL * Platelet count ≥ 100,000/μL * Hemoglobin ≥ 8.5 g/dL * Total bilirubin ≤ 1.5 times upper limit of normal (ULN) * INR ≤ 1.4 times ULN * Creatinine ≤ 1.5 times ULN * Thyroid-stimulating …