Backing up these claims is a three year warranty. I've worked on Logitech stuff for years and it is typically very up to spec.
There are several reports of a problem where the normally green blinking charge light alternately blinks red and green. One solution is to contact Logitech and get their experience on this.
But you could try a few other things first. The hassle is in proportion to the gain. My thesis is that if a battery says it's charged or throws an error, it's more likely due to a signal from the temperature pin of the battery or a change in the charging current or suchlike. These occurs in situations other than "it's broken or dead". Here's what I do when I think the keyboard is sick, rather than terminally ill:
a) Repeatedly put the keyboard in and out of the charging dock. Try this with the keyboard either off and then on. One way or the other, you might be able to recharge it. This worked for me.
b) Drain the battery (put a weight on a Fn key) and see if you can better charge from this empty state. This also worked for me.
c) If the red / green flashing recurs leave the keyboard somewhere cold. Then charge till you see an error, then cool and repeat. This worked for me and we were working good for months at least.
d) Not tried yet and I'm keeping this in reserve: use a different power supply to get enough juice in the battery to make it happy again. As with over-discharged mobile phone batteries, a higher or lower charging rate can knock some sense into them. Monitor this in case the temperature goes awry.
e) I have not tried to replace the battery. The battery is not soldered to the board, however removing the orange underside will make a mess of it. I'm saving this for a desperate moment.
[UPDATE: After successfully using the tricks on this page over a few years, I ran out of luck, the red-green flashing continued and my desperate moment had arrived. I followed a Youtube video to use a hairdryer to remove the orange underside; then undo several screws and ultimately to swop the battery for a new one. The 'new' battery actually came from an old Sony camera. This has been a huge SUCCESS as the keyboard now hold a charge and also charges with ease.
f) Some folk suggested to unpair the keyboard, reinstall the (optional) Setpoint monitoring software or hitting various keystrokes. I suspect these are accidentally useful.
