What happens when a pet you want to create is "limited"? Can you never make that pet again? Or does it come back in a while?

It just means it isn't 'in stock' so to speak. You will have to wait awhile until they release more for you to create.

However it is pretty easy getting pet species from using elixirs (e.g.: Lilac Sheeta Elixir for Sheetas) or in Cadogre's case, Mystical Toys.

Thank you!