Pazopanib Hydrochloride After Leuprolide Acetate or Goserelin Acetate in Treating Patients With Relapsed Prostate Cancer

Inclusion Criteria: * Histologically or cytologically confirmed prostate cancer * Stage D0 * Must have undergone some definitive local therapy for prostate cancer * Must be free of macrometastatic disease, as evidenced by computed tomography (CT) scan and bone scan, if serum PSA ≥ 10 ng/mL prior to GnRH agonist therapy * Progressive disease meeting the following criteria: NOTE: Patients who have undergone a prostatectomy and have two detectable, rising serum PSA levels are eligible * Two consecutive rises in PSA above nadir recorded after definite local therapy * Serum PSA concentrations must have absolute value of \> 0.5 ng/mL (separated by ≥ 2 weeks) prior to beginning GnRH agonist therapy * PSA \< 0.5 ng/mL * Testosterone \< 30 ng/mL * No measurable disease * No brain metastases requiring steroid or anticonvulsant therapy * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2 OR Karnofsky PS 60- 100% * Prothrombin time (PT)/international normalization ratio (INR)/partial thromboplastin time (PTT) ≤ 1.2 times upper limit of normal (ULN) * Bilirubin normal * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 times ULN * Creatinine ≤ 1.5 times ULN OR creatinine clearance \> 50 mL/min * Proteinuria ≤ 1+ on 2 consecutive dipsticks \> 1 week apart * Urine protein: creatinine ratio \< 1 OR urine protein \< 1.0 g/24 hours * Fertile patients must use effective double-barrier contraception during study therapy OR completely abstain from sexual intercourse 14 days prior to, during, and for ≥ 21 days after completion of study therapy * No history of allergic reactions attributed to compounds of similar chemical or biological composition to pazopanib hydrochloride or to other agents used in the study * No concurrent uncontrolled illness including, but not limited to, any of the following: * Ongoing or active infection * Psychiatric illness or social situations that would preclude compliance with study requirements * No human immunodeficiency virus (HIV) positivity * No condition that impairs the ability to swallow and retain pazopanib hydrochloride tablets, including any of the following: * Gastrointestinal tract disease resulting in an inability to take oral medication * Requirement for intravenous (IV) alimentation * Prior surgical procedures affecting absorption * Active peptic ulcer disease * No other conditions, including any of the following: * Serious or nonhealing wound, ulcer, or bone fracture * Abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 28 days * Cerebrovascular accident within the past 6 months * Myocardial infarction, admission for unstable angina, cardiac angioplasty, or stenting within the past 6 months * Venous thrombosis within the past 12 weeks * New York Heart Association (NYHA) class III or IV heart failure * History of currently treated asymptomatic NYHA class II heart failure allowed * Systolic blood pressure (BP) ≤ 140 mm Hg and diastolic BP ≤ 90 mm Hg * Prior initiation or adjustment of BP medication allowed provided that the average of 3 BP readings at a visit prior to enrollment is \< 140/90 mm Hg * More than 3 months since prior antiandrogen * More than 4 months since prior orchiectomy or implantable luteinizing LHRH agonist * No prior GnRH agonists except for neoadjuvant or adjuvant therapy associated with local therapy * Patients who have started a GnRH agonist for micrometastatic disease after local therapy allowed provided the following criteria are met: * Progressive disease * Willing to discontinue therapy before 6 months have elapsed * Have signed consent prior to completing 6 months of the initial hormone therapy * Are within 4 months of initiating GnRH agonist therapy * No prior or concurrent GnRH antagonist therapy * No concurrent ketoconazole * No concurrent cytochrome P450 2C9 (CYP2C9) substrates, including any of the following: * Anticoagulants (e.g., warfarin \[therapeutic doses only\]) * Low molecular weight heparin or prophylactic low-dose warfarin allowed * Oral hypoglycemics (e.g., glipizide, glyburide, tolbutamide, glimepiride, or nateglinide) * Ergot derivatives (e.g., dihydroergotamine, ergonovine, ergotamine, or methylergonovine) * Neuroleptics (e.g., pimozide) * Erectile dysfunction agents (e.g., sildenafil, tadalafil, or vardenafil) * Antiarrhythmics (e.g., bepridil, flecainide, lidocaine, mexiletin, amiodarone, quinidine, or propafenone) * Immune modulators (e.g., cyclosporine, tacrolimus, or sirolimus) * Miscellaneous medications (e.g., theophylline, quetiapine, risperidone, tacrine, clozapine, or atomoxetine) * No concurrent medications associated with the risk of QTc prolongation and/or Torsades de Pointes * Replacement of drugs that do not carry these risks allowed * No other concurrent non-Food and Drug Administration (FDA)-approved agents