Many thanks for your patience, I am pleased to be able to continue assisting with your query now. Generally, when a person places an order for something, be it goods or services, and pays a deposit, they enter into a legally enforceable contract with the other side. It is implied that the provider has accepted the deposit as security and as proof that the customer wants to proceed with the contract.
Unless the provider subsequently commits a serious breach of contract, such as failing to supply the goods or services, they are the ones cancelling the contract, or there was a cancellation clause, the customer would have no automatic legal right to cancel the agreement. If they do so they will likely be acting in breach of contract and potentially risk losing their deposit.
Whether the deposit can be retained will depend on what the effects of the cancellation were. In general, the deposit can only be used to cover any actual and unavoidable losses incurred as a result of that breach. It could be administrative costs, some loss of profit, etc.
If this was a business retailer, they will be subject to the Consumer Rights Act 2015. That will make retaining part of the deposit, over and above the losses which they have incurred, unlawful as it would be an unfair contractual term.
So if you can sell the puppy to another buyer, even if not immediately, you would have recuperated most of your losses and can only potentially retain part of the deposit to cover administrative costs, such as extra charges or adverts and a difference in price, if you had no option but to sell it for a lower price in order to facilitate a sale.
Hopefully, I have answered your query in a way that is simple and easy to understand. If anything remains unclear, I will be more than happy to clarify it for you. In the meantime, thank you once again for using our services.