The description of the Scapular on the wiki says:
Whenever you are downed to 1/2 of your last Heart, Aura around your head temporarily vanishes and you are granted 1 Soul Heart.
Does this effect have any kind of cooldown? Is it a one time only?
The effect did not have any cool down that I could notice and is definitely not one time only. It saved my hide multiple times in adjacent rooms (I was careless).