I'm thinking maybe the reason for the deposit is to get people to actually attend and not just say they'll come. Then when the day comes and the teacher is there and everything is a "go," no one shows up because they had something else to do.
Could you talk to this lady privately and state your concern over not getting a refund if something really, truly horrible prevents you from attending (death in the family, an illness, etc.)? Maybe she'll think about it and amend the refund policy.