The challenge page says these are awarded every 12 hours. Is there a particular time of day that they checks are made?

For any of the challenges, go to the challenge and you'll see the number of winners on the bottom of the page. Click on the number. That will give you a list of the most recent winners and the time and date the badge was awarded. That will give you a good idea of when to expect a new badge.

Thanks, Tizzabelle. That had never occurred to me.

Brain joke deleted...