Read with great care the applecare document for your MBA.
It might depend on where you are in the world. And the particulars at the time you purchased the applecare.
I know this discussion has come up before that Apple were refusing support for accessories even when purchased at the same time.. In which case consumer law is on your side.. because you bought extended warranty which is not being honoured.
I dug out the applecare doc for US.
APP Mac - North America English
specifics you need..
3.2 Covered Equipment
In addition to the Apple-branded product and accessories contained in the original packaging, “Covered Equipment” includes the following according to your Plan:
ℹ Under APP for Mac, (a) one compatible Apple-branded display if purchased at the same time as the Covered Equipment, (b) an Apple-branded mouse, Magic Trackpad, Apple Battery Charger and keyboard if included with the Covered Equipment (or purchased with a Mac mini or Mac Pro), or (c) an AirPort Express or AirPort Extreme Base Station, AirPort Time Capsule, Apple memory modules (RAM) and Apple USB SuperDrive if used with the Covered Equipment and originally purchased by you no earlier than two years before the Covered Equipment purchase.
(ii) Under APP for Apple TV, an AirPort Express or AirPort Extreme Base Station and AirPort Time Capsule if used with the Covered Equipment and originally purchased by you no earlier than two years before the Covered Equipment purchase.
If Apple are not honouring their warranty and applecare protection agreement.. take them to the consumer protection authority in your country.
The cover is stated clearly in the document.
Unfortunately Apple have occasionally needed some help in reading their fine print.