Yes, you should be concerned. first, be sure your breeder is a certified breeder, fully licensed. Some of them will claim to be, but when you get them into court, they use a trick where they state they aren't a breeder, they only have 12-14 animals they sell a year (this is an attempt to get around the laws dealing with breeders. Most states vary, but above a certain number of animal sales, they're considered breeders. They attempt to cicumvent this with these claims).
Second, demand to see the vet report that states the kitten has been cleared of all diseases and illnesses, hereditary or otherwise. I'd check the paperwork you signed to see what it claims as well.
You're in the unusual position of having paid a deposit and the breeder is stalling for reason that may or may not be legitimate (supposedly non refundable).
The law states that a non refundable deposit in a contract is returnable if either party is in breach. In this case, there's a reasonable expectation that the kitten will be given to you after it's second vaccination.
If this health issue is due to a simple cold (it could be) then it should be cleared up in a week. now, it's up to a judge to interpret, but most would say if 4-8 weeks have gone by and you haven't received the merchandise (kitten), then the breeder has violated the spirit of the contract and the refund must be returned.
Be aware that the law provides only about 14 days from the actual receiving of a pet to do a return. There's a whole section of legality I won't get into here in a case of a pet that is "past the expiration date" or a pet that has an illness, and suing for vet costs, etc... that I won't get into now (hopefully you won't have to deal with that!)
But since you haven't received the kitten yet, this doesn't apply. Provided this IS a breeder.
This is important; if the breeder and you decide to go with a DIFFERENT kitten, you must redo the contract. DON'T roll over the refund. This time, read it carefully. If he won't do that, demand your money back. In this case, HE is in breach of contract and the non refundable status is void.
Thank you so much for your reply. It has been incredibly helpful to me.
No worries. Let me know how the whole thing works out, and if you have any other questions. Animal breeding has the best an the worst, just like every other industry. The law is finally catching up in terms of regulation, but it does still need some work.