Is your Nexus 7 no longer in charge of its battery?

Betteridge’s Law might not apply here. It didn’t to me.
I was the owner of a new Google (slash-Asus) Nexus 7. And I rather liked it. I liked it a lot more once I found out the previously suggested lack of USB OTG capability turned out not to be true- a review later on.
I liked it right up until the point that my N7 stopped charging. Or did it? The battery meter was suggesting that I could not get off the 77% mark, despite also showing I was on AC power. But then it also didn’t drop below 77%.