I don't know that Apple will change batteries in models that they've stopped supporting. (They don't actually change the batteries in your iPad, they just hand you a refurbished unit, transfer the data over, and then send yours in for refurbishing).
I can't see apple refurbishing 5 to 10 year old models and keeping them in stock in case someone shows up with a 'moldy oldy' that needs batteries... Unfortunately, it's gotta end sometime
I kept my iPad 1 when I last upgraded to the Air.. It's going on 4 years now and still has surprisingly good battery life.