What kind of fallacy is committed when people keep ignoring refutation of their premises?

Suppose Smith uses P as a premise. He keeps using it even after it is criticized and refuted. What fallacy does he commit?

This kind of behavior is generally seen as a cognitive bias or even a departure from the reasoning process (rather than an error within reasoning). A clear refutation deserves acknowledgement or at least a counter refutation (a refutation of the refutation). A strong confirmation bias might lead to the person overlooking the obvious refutation to protect him or her from being wrong. Or, the person might be aware of the strong refutation, and simply ignore it because they are more interested in the perception of being right than in the truth. This essentially breaks the rules of argumentation and honest dialectic with a basis in reason.

Willful Ignorance. When that occurs, you can't reason w/ people like them. And you've got to move on.