The only place where the flag is never flown at half-mast – is the moon.
By the way, the toughest moonwalk task may well have been planting that flag. NASA’s studies suggested that the lunar soil was soft, but astronauts Neil Armstrong and Buzz Aldrin found the surface to be a thin wisp of dust…over hard rock. They managed to drive the flagpole a few inches into the ground and film it for broadcast, and then took care not to accidentally knock it over.
On an additional trivia note, the flag was made by Sears, but NASA refused to acknowledge this because they didn’t want “another Tang.”