That said, I'm not sure he can complain that a recurring subscription continued to, well, recur.
Yes, I will complain. Intrinsic in the notion that I'm not bothering to update billing information after numerous updates telling me that it will cancel if I don't is the conclusion that the service, and billings, will cease. Credit cards have expiry dates for a reason, and ultimately it is fraud that they effectively manufactured my info for me.
I'd check the wording of those updates. It's usually that your service may be interrupted if you fail to update your credit card when it expires. And usually, the terms of the site say that you're on the hook for the recurring charge even if your card fails to clear.
You're hoping that the natural expiration cycle of your physical card - not the account - will impact a transaction that doesn't actually involve that physical implement. I can see where you're coming from, but I don't know that you really have a right to expect the expiration of your physical card to impact an existing business relationship with a third party that involves recurring charges (that you have likely agreed to pay regardless of your card's validity, or credit limit.)
I've worked on these kinds of renewal systems for large sites and generally, users don't mind them because the reverse case - where 4% of the users lose access each month because their physical card expired - sucks for both the site and the end users who don't expect access to be cut off.
If you want to use credit card changes as a shortcut for properly cancelling your subscription, you probably need to actually change the card number.
Yes, I will complain. Intrinsic in the notion that I'm not bothering to update billing information after numerous updates telling me that it will cancel if I don't is the conclusion that the service, and billings, will cease. Credit cards have expiry dates for a reason, and ultimately it is fraud that they effectively manufactured my info for me.