This study will investigate the safety and effectiveness of the drug TNFR:Fc to treat uveitis (eye inflammation) in patients with juvenile rheumatoid arthritis. In other studies, TNFR:Fc significantly reduced joint pain and swelling in adult patients with rheumatoid arthritis, and the Food and Drug Administration has approved the drug for that use. Because medicines for arthritis often help patients with eye inflammation, this study will examine whether TNFR:Fc can help patients with uveitis.