Hello and thank you for your question.
Whether you can get your deposit back depends on what the contract states and if the breeder has fulfilled the terms of the contract. If the contract has a clause which states that it is intended to contain all the terms between the parties and/or that the terms of the contract can only be changed by a writing signed by the parties, then it cannot be added to by verbal agreement or disclosure
such as the deposit being non-refundable. You can then argue that the deposit is refundable.
If it does not contain such a clause and if the breeder informed you at the time that you made the deposit that the deposit was non-refundable, then you would have a difficult time arguing that it wasn't part of the agreement even though it is not written in the contract. If the seller did not disclose that the deposit was non-refundable and it is not included in the written contract then it is not part of the contract because there was no meeting of the minds with regard to that term. You would then have an argument that the deposit is refundable.
Also, if the puppy was not as represented or if there was some other breach of the contract on the part of the seller, then you would also have basis to get your deposit back. However, because you characterize the issue as a problem with a clause in the contract or "oddity" in the contract this would likely not constitute a breach and the law would likely be on the breeder's side to enforce the contract, including the non-refundable deposit if it was revealed to you. If the "oddity" in the contract is itself illegal, then that term and perhaps the entire contract would be void and unenforceable and you could get the deposit back.
These would be the available legal arguments that you could use to resolve this matter with the breeder. Please feel free to ask any follow-up questions.