The Kindle is approximately 18 months old. It was ordered brand new from Amazon for a UK Mother's Day gift last year (3rd April), but it has only been used regularly for around a year. I can't vouch for how often it has been charged, e.g. if it was only charged when the battery got low, or if it was frequently "topped up" which I understand isn't the best thing to do with the type of battery this Kindle model uses.
It hasn't displayed any low battery warning messages at any time while this recent problem was happening, but I guess that may not mean anything if it is indeed faulty.