I had a problem with a non-fucntioning right Airpod. It did not show the alert above, it just didn't connect or appear in the Battery widget on my iPhone.

I noticed that replacing the Airpod in its case did not trigger the charging light, so I deduced that the case didn't recognize the Airpod was there. That gave me a possible cause: the metal charging contacts were not touching the airpod when inserted, so the airpod had run out of battery, and the case wasn't charging it.

I was able to bend the contact back into shape with a paper clip (not easy due to the shape of the cae & the strong magnets) but when I was done, the Airpod quicky charged and worked as normal again.

As of this writing, Apple's online support was not able ot figure this out & only offered a replacement right airpod.