I'm not saying that everything is great, as it certainly is an inconvenience for both of you. They lost the day of work too. Im sure they would rather have been working and making money too.
Also, the deposit is there to protect the artist. It will still go towards your overall cost. All you can do is reach out and state explicitly that you will or will not be at the next appointment.
Again, this is certainly less than ideal. All i was trying to say was that this hardly seems to be worth this amount of online stressing and venting.