Explain how Abigail's disappearance affects the resolution of the play The Crucible?

Abigail's disappearance tells you everything you need to know about this devious, slippery character. Having unleashed all this chaos upon Salem, she's nowhere to be found as the action of the play heads towards its tragic conclusion. However, instead of concluding that Abigail was a pathological liar and that the witch-trials based on those lies have no credibility, Judge Danforth still goes ahead with the proceedings despite Reverend Hale's desperate pleas. What this shows us is that, although Abigail may have started this particular fire, others have a vested interest in keeping it going. There's simply too much riding on a successful outcome of the trials (i.e., sending innocent people to their deaths) to stop them now. It's as if the whole witch-craze has taken on an unstoppable momentum all of its own, and which must be allowed to run its natural course.

Abigail's disappearance makes plain her dishonesty and deceptiveness, something the courts have been unwilling to see up until now.  She lies to her uncle, telling him that she'll be spending the night at her friend, Mercy Lewis's, house -- Mercy tells the same lie at her house -- and then Abigail robs her uncle blind.  Before boarding a ship, she breaks into Reverend Parris's strongbox, and steals his life's savings.  It begins to look as though Abigail is not the righteous, holy, instrument of God the courts initially believed her to be; instead, she appears to be a conniving and deceitful young woman, determined to serve herself and get out of Salem before the tide turns against her.
Abigail's dishonesty casts doubt on the accusations she has made thus far.  Her disappearance is just one of many reasons, however, that Reverend Parris and Mr. Hale beg Deputy Governor Danforth to postpone the hangings.  Despite the many reasons to delay, Danforth refuses, insisting that it will only cast doubt on the guilt of others who have been hanged for the same crimes already.  He seems to understand, now, that Abigail is a vicious liar, but he will not risk his credibility or authority by walking back on the convictions.