Goldstein's influence never declines and the government never captures him because his existence is vital if the government is to survive. In fact, it is not clear that Goldstein really exists. He may, in fact, have been made up by the government.
So why does the government need him? One of the main ways the government keeps society together is by having something for them all to hate. This is Goldstein's function and it is one reason why Ingsoc is always at war.
Without a bad guy on whom to focus, the people might not be so united and they might start to think about how their lives aren't that great. So the government needs Goldstein to keep the people from being discontented.