In Act 3 of The Crucible, what can't Mary Warren do when asked by Parris and Danforth?

In act 3 of Arthur Miller’s The Crucible, Reverend Parris and Judges Danforth and Hathorne command Mary Warren to faint to prove her previous fainting spells were false. However, under their pressure and the weight of being exposed in court, she cannot do it.

John Proctor has brought Mary Warren to court to help him free his wife who has been accused of sorcery by the teenage girls in the village. Mary had been one of the accusers, and her testimony was instrumental in the arrest of John’s wife Elizabeth. Now Mary claims that the girls, led by Abigail Williams, made it all up.

Danforth: Then you tell me that you sat in my court, callously lying, when you knew that people would hang by your evidence? (She does not answer.) Answer me!

Mary Warren: (almost inaudibly) I did, sir.

Danforth and Parris are not easily convinced by Mary’s retraction. They have invested weeks of their time and great effort into these trials and will need to be convinced. Danforth presses Mary to see how committed she is to her new story.

Danforth: Now, children, this is a court of law...It does not escape me that this deposition may be devised to blind us; it may well be that Mary Warren has been conquered by Satan, who sends her here to distract our sacred purpose...But if she speak true, I bid you now drop your guile and confess your pretense, for a quick confession will go easier with you.

Mary sticks to her story, but Abigail remains firm in her denial of wrongdoing. As Danforth tries to determine who is truthful and who is lying, Judge Hathorne seizes on what he believes to be evidence that Mary is lying. He and Parris recall her behavior during her previous accusations:

Hathorne: (with a gleam of victory) And yet, when people accused of witchery confronted you in court, you would faint, saying their spirits came out of their bodies and choked you—

Mary Warren: That were pretense, sir...

Parris: But you did turn cold, did you not? I myself picked you up many times, and your skin were icy, Mr. Danforth, you—

Proctor: She only pretended to faint, Your Excellency. They’re all marvelous pretenders.

Hathorne: Then can she pretend to faint now?...let her turn herself cold now, let her pretend she is attacked now, let her faint. (He turns to Mary Warren.) Faint!

Mary Warren: I (She looks about as though searching for the passion to faint. ) I—have no sense of it now, I...I—cannot do it.

Mary insists the fainting was all part of the falsehood, so they logically demand that she reproduce the false faint to prove that she can make herself appear to pass out. Unable to do it, she claims to have “no sense of it.” In this moment, she lacks the emotional frenzy stirred up by Abigail and her minions that Mary drew upon to make herself faint. When she is not being dominated by the force of Abigail’s personality, her resolution crumbles and her story falls apart.

Mary Warren has admitted to faking the sighting of the devil, the fainting, the chills, the shaking. John Proctor brings her into the court room to prove the girls are lying, but Mary is unable to fake seeing the devil, perhaps because Abigail was their leader and was able to "act it" better than the other girls, and lead them into believing.

In Act 3 of The Crucible, what can't Mary Warren do as requested, and Judge Hathorne's point about it?

In Act III, Mary Warren tries to confess she was lying the last time she testified in court. Previously, she claimed she only pretended to faint.  In order to prove this, Judge Hathorne asks if Mary Warren can "pretend to faint now," and Reverend Parris orders her to do so.  Although she "looks about as though searching for the passion to faint," Mary Warren claims she has "no sense of it now."  This leads Deputy Governor Danforth to assume Mary Warren cannot faint now because there are no spirits loose in the courtroom.  Again, Mary tries to "[search] for the emotion of it," but without the other girls screaming, the heightened emotion of them all acting together, Mary finds she doesn't know how to pretend to faint alone. 

Mary Warren's second experience testifying in court is very different from her previous one. Now, everyone stares at and questions her as though they suspect her of lying.  Mary tries to explain her prior behavior, saying, "I heard the other girls screaming, and you, Your Honor, you seemed to believe them, and I — It were only sport in the beginning, sir, but then the whole world cried spirits, spirits."  Without the incredibly heightened emotion of a trial, without the group all around her acting as one, Mary simply cannot pretend as she did before.  As a result, the magistrates do not believe her, which is terribly ironic given the fact that this is the first time Mary's told the truth in court.

When asked to pretend to faint, Mary is unable to do so. The judge makes the point that if she cannot pretend to faint at that point then perhaps she did not pretend to faint before. This casts a lot of doubt on Mary's claim that Abigail and the rest of the girls are also pretending. Mary's credibility is also destroyed and eventually she rejoins Abigail in making accusations against John Proctor.

Why can't Mary do what Parris and Danforth ask in Act 3 of The Crucible?

I think you are referring to the part in Act III when Mary is asked to faint like she had done in court on the other days. Mary now says she was pretending to faint, so Danforth wants her to pretend to faint now. Mary can't pretend to faint at this point because she isn't caught up in the moment of court when the other girls are screaming, and "the whole world cried spirits, spirits,. . ." Mary follows the lead of the other girls, screaming and crying and pretending to see spirits. "I--I heard the other girls screaming, and you, Your Honor, you seemed to believe them, and I--It were only sport in the beginning, sir,. . ." It was fun at first for Mary, but she never dreamed the girls would be believed by the adults. When the ministers and judges believed what they were saying, the girls took it farther because now they had power, something Puritan children usually did not have. Mary realizes she can't convince the court it was all pretense when Abby and the other girls start accusing her of being a witch.