I agree with Linda - I wouldn't give in and let her out again. They learn things so quickly (i.e. if I cry, they will play with me). Can you put a toy or treat in the crate with her when you put her back in (at 4 am)? I would keep working at trying to get her stay up a bit later in the evening...maybe a nap around 6 or 7 pm so that she will be awake later on?