In The Crucible, Danforth represents a "popular mode of power". He makes many of his most important decisions, not based on justice, but based on public perception. 

Danforth is given testimony from Proctor that clearly demonstrates the falseness of the witchcraft claims made against many of the people of Salem. Reverend Hale also begs and argues for the release of the accused, saying that the trials have been a fraud. 

The popularity of the belief in the idea that the witchcraft is real makes Danforth hesitate to reverse his decision. He is unwilling to go against the majority (despite the prominence of his position and the authority invested in him to act justly). He fears losing face and suffering a dimunition of stature. 

In addition to these concerns, Danforth argues that the court has already set a course and a precedent. Some people have already been put to death as a result of the trials. 

He argues that it would reflect badly on the court if he released prisoners after executing a number of people accused of the same crimes—regardless of their innocence.

To maintain the stature of the court and to protect his own reputation, Danforth is unwilling to publically recognize the reality of the situation in Salem. 

Why does Danforth refuse to consider a postponement in The Crucible?

Danforth in Act IV is a character who can only be described as implacable. He refuses to postpone the hanging of Proctor, Rebecca Nurse and Martha Corey, even though there is clear proof that Abigail was not genuine and that the witchtrials in nearby Andover have ended in riots as the court was overthrown. Yet Danforth continues on his path, no matter what others think or say. Note how he justifies his actions:

Postponement now speaks a floundering of my part; reprieve or pardon must cast doubt upon the guilt of these that died till now. While I speak God's law, I will not crack its voice with whimpering.

Danforth is obsessed with the idea that he is appointed to be God's judge in this place, and therefore to admit that he was wrong or to deviate from his course would reflect badly on God. There is no question of the truth or what is right to do. To Danforth's mind, now that judgement has been pronounced against these characters, they must die, regardless of whether they are guilty or innocent.