Wireless keyboard

What should I do with a Mac Wireless keyboard when the green light continuously blinks and doesn’t respond to an off command, pairing or anything at all? The only thing I can do is take the batteries out and even then when I put them back in after an hour or even overnight the light just starts blinking again as if nothing had been done.

Previously it had been paired to an Apple TV (as well as an iMac, but that isn't the usual arrangement) with no problems, but it had been turned off for some time. When I went to use it again the above started to happen. I changed the batteries thinking that they might be drained and that this was the keyboard’s way of telling me that but, apparently, that wasn’t it.

So what might it be?