It sounds like he's fallen into a bad habit. He's asking a question that he knows, at some level, is silly. But there's a bit of a compulsive element to it. My guess is that he's acting on an underlying anxiety, and asking an unreasonable question makes him feel more in control.
In these sorts of situations I try to diffuse the dynamic by being confident and inject a little humor. If you understand that his question isn't coming from reasoning, but from anxiety, then you can address that better indirectly than directly.
In situations like this, I usually allay the fears of management by presenting all the measures I've taken to ensure quality. He is, after all, the customer, and he needs to know that your priorities are in line with his. Look at these unit tests. Look at this monitoring. Look how the code is structured to keep changes local and modular. etc. If you convey a sense of confidence and control, it will allay his anxiety and you'll probably be able to have a more rational conversation.
That's where the art of this business comes into play. Not just "does it work", but does the customer feel good about it.
Ultimately, though, it's a business relationship. If the contracting arrangement is comfortable and profitable for you, then putting up with this quirk is worthwhile. It doesn't sound like he's all that serious about it, just kind of persistent. Like I say, he's developed an annoying habit. If he begins to react adversely and the tone becomes more hostile, then the balance of the business arrangement may make it not worthwhile for you. But from your short description, it sounds to me like you can still manage the relationship effectively.