Why is the court so hesitant to believe mary warren and john proctor? what would they lose if the trials stopped?

They were reluctant because Mary and John’s motives were suspicious - they suddenly appeared in court to tell the ‘truth’. They [the court] were suspecting that since Elizabeth [Proctor] was arrested, John Proctor forced Mary to do it and it was against her decision to tell the story about the witchcraft that saved the life of John’s wife. If they stop the trial, they would not be able to solve this mysterious case at all.