Why doesn't Elizabeth take Hale's advice?

Elizabeth doesn't take Hale's advice because she refuses to make her husband concede to the wishes of others, especially if it means he will have to ruin his own reputation in the process. Regardless of their problems, Elizabeth knows her husband to be a proud man, and she understands his need to stand the moral ground, to guard his reputation, even when it meant he had to tarnish his reputation (admitting to adultery) in the process.