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Actually they can change the batteries in your iPad and return the same iPad to you. They've not announced anything yet about no longer servicing the iPad 1. Until they do, Apple will still service them.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.