A non-refundable deposit is legal: there is no requirement in the law that deposits be refundable, and in fact, they are usually only refundable if it is specifically stated that they are or if the provider (i.e. the dentist) cancels the work. If the customer (you) cancels the work, the provider is generally allowed to keep the deposit. That is the entire point of a deposit after all: to give the provider an incentive to reserve time for you and prepare for what has to be done, by assuring them that if you cancel, they will still receive payment. Your cancellation of the work is a breach of the agreement that they would perform work on you and you would pay for it; your breach lets them keep the deposit.