I have noticed that my Edge 1030 sometimes doesn't shut down when I press "Power Off". It just shows the screen with the power symbol continuously.
The first time this happened, I ignored it, and the next day when I was ready to ride, the Edge was down to 30% battery level. I've paid more attention since, and if it doesn't shut down after about 30 seconds, I press the On/Off button and the Lap button simultaneously until the unit restarts, and do the "Power Off" operation again.
So far, it has always powered off on the second try.