Why is it that Proctor will not back down after Elizabeth has been given one more year to live?

To save Elizabeth and protect himself from an inevitable accusation of witchcraft, Proctor must tear down his name and condemn himself for the crime of lechery. Despite Proctor's obvious sin, this places Proctor as a martyr, sacrificing any chance for a good reputation in Salem, where public reputation is essential, in order to save his wife and others wrongly accused of witchcraft.