Why does Beatrice not defend her cousin from Claudio's accusation in Much Ado About Nothing?

Beatrice does not defend Hero because she is a woman, so she asks Benedick to do it.

Beatrice does defend her cousin, but not in the way you are thinking.  She does not jump up and shout during the wedding that Claudio is wrong.  That would be unladylike.  You have to remember that things were different in those days. A woman just did not have the same clout as a man.  He won't listen to her.

What Don John did was terrible, but so was what Claudio did.  Claudio defamed Hero publicly.  He destroyed her reputation.  They fake her death, but he might as well have killed her.  That was it.  For a woman in those days, your reputation was your life.

Beatrice is a woman.  Nothing she said at the wedding would have made any difference.  Not only did Beatrice not stand up for Hero when Claudio spoke up, you notice that no one did.  Her father didn’t stand up for her, and neither did Benedick.  Hero’s character had been spotless up until this point, but the moment it was in doubt no one questioned it.  Everyone took Claudio at his word.

The friar believes Hero, and for some reason he seems to be the only one.  Benedick is willing to go along with it.  After all, he is in love with Beatrice and will want to make her happy. 

BENEDICK

Sir, sir, be patient.
For my part, I am so attired in wonder,
I know not what to say.

BEATRICE

O, on my soul, my cousin is belied!

BENEDICK

Lady, were you her bedfellow last night?

BEATRICE

No, truly not; although, until last night,
I have this twelvemonth been her bedfellow. (Act 4, Scene 1)

Beatrice is feisty.  There may have been nothing she could do at that point, but that does not mean she will do nothing at all.  She has a card to play.  She has a man that she can manipulate—Benedick.  Beatrice gets Benedick to defend Hero’s honor.

Beatrice tells Benedick that he needs to do something about this.  She tells him that she wants him to get satisfaction from Claudio.  Claudio, you must remember, really does believe that he is the one in the wrong here.  Oh yes, it is a tangled mess.  However, Claudio did not sufficiently investigate the situation before publicly denouncing his bride, so the blame lies with him.