What is the significance of Hale's loss of confidence as the play progresses into Act II?
I don't think that Hale experiences a great deal of losing confidence into Act II. He approaches John Proctor with the suggestion that he get his child baptized and that he "get right" and attend church more frequently. When Elizabeth is arrested, Hale is quick to say that the court will clear her. He does not necessarily stop Cheever from doing his duty. He thinks that there is an answer and believes that the faith in the religious order of Salem is that answer.
I believe that the real loss of confidence is evident during the trial in Act III. For example, when he has to sign the death warrant for Goody Nurse, he expresses his own sense of discomfort to Danforth. At the same time, he is increasingly weary of how the court is conducting itself and, of course, Abigail. It is herre where Hale's loss of confidence is evident and significant in that he no longer can stand up what is being done.
In contrast, I would say that the significance of Act II's conception of Hale represents how individuals who fail to question their authority when they feel something is wrong actually end up being complicit to it. In this, I think that there is much significance in Hale's support of what is happening in Act II.
As the play continues, Hale begins to doubt the veracity of Abigail and her charges of witchcraft. He is an outsider who has been asked to be part of the investigation. As he gets to know John and Elizabeth Proctor, he finds them to be honest and believable. Judge Danforth won't admit he might have made a mistake in listening to Abigail and the other girls over Giles and John Proctor since he has already sent several to their deaths. By the last act, Hale denounces and quits the court and begins to counsel the accused to lie in order to save themselves from the corrupt proceedings. However, John Proctor, Rebecca Nurse and a few others choose to die to protect their good names and reputations.