A:
Had a similar problem with the keyboard I purchased back in 11/2011. If you haven't already found a solution, or tossed it in frustration, you might want to try replacing the rechargeable battery.
YouTube has multiple videos on how to do it. The keyboard uses a Maxell ML2032 rechargeable coin battery. While they offer replacements on their website, it always seems to be out of stock. so you will want to Google other sellers. Remember that it has to be a rechargeable battery. Single use batteries won't work without modifications to the keyboard that you don't want to make.