why is ann willing to remain silent about joe?

Like her husband, Mother is in denial. She knows about Keller's guilt, and it is the source of her anxiety and headaches throughout the play. She is complicit in Keller's denial, and as for her own denial, she is forcing her son to stay alive, if only in her mind, in order to allow her to continue to live with her husband in some acceptable way. That is, if she had to accept that her husband effectively killed their son, then she could not bear it. But her loyalty to Keller ironically serves to separate the couple, since her knowledge of his guilt strains their relationship. Like her husband, she prefers to believe that there are forces outside her control--in her case, astrology and God's choice, both on Larry's side--that ultimately dictate life or death more than individual choice does.