In Act IV of The Crucible, why won't Danforth pardon the prisoners?

At this point, even Danforth understands that the whole
witchcraft hysteria was probably a hoax, and that he and the Puritan court had sent
innocent people to their deaths.  By Act IV he is trying to save face by urging them to
confess so he can let them off the hook.  But Proctor and the others aren't interested
in lying to save the church's credibility or pride.  This is frustrating to Danforth,
and he feels like he has to follow through on the hangings then, or he would be
essentially confessing his awareness of the hoax.  He is truly in a no win situation by
this point.