Could it possibly be an issue with the lightning cable and not the charger itself?
Here is also another suggestion to figure out what may be causing the problem: Are you are using any third-party products to charge your phone? Or only an Apple Lightning cable and charger?
If you are using a third-party lightning cable, even if it is Mi-Fi Apple certified, sometimes your device will suddenly stop recognizing it. You will get that same “Device [the cable] not supported/recognized” message. This has happened to me on different devices, over several iOS versions. (Using third-party cables from several well-respected brands, too) It may be similar problem.
Disconnecting and reconnecting the cable (often multiple times) from my iOS device occasionally succeeded in the connection working again, at least for a short time. More often it never worked again. Unfortunately, I never found long-term fix, except to buying a new cable.
If you are only using Apple accessories, I’m sure you know lightening cables are fragile and can be easily damaged or stop working. So, it could still be a cable issue.
If you have an AppleCare(+) warranty, you should contact them directly to check about trading in a bad Apple cable (or charger) for a replacement.