Do you have the email they originally sent you with the list or link to available dates? If so look at it and give multiple options from that list of times you can reschedule to. Things come up. They just do. Yes they state that the importance of the schedule because it is a pain to reschedule. But if you're open about what happened, apologetic, and tell them you're willing to work to make it right, I think a decent human being would give you another shot. If you can't do it on the original date then they still have a shop to do, so if you can get it done then at least they're not starting over looking for another shopper.
The scheduler/editors for these shops seems really nice. My experience with them is limited, but I have nothing but good things to say about them.