I'm using an iPad Mini 4, by the way.
Whenever I break a block with a door, or stack of doors, in hand the doors lose durability like a pick-axe or other tool. On top of this, attacking mobs with a door decreases their durability. Doors with durability shown do not stack with others, and placing and re-destroying a door resets it's durability. I've only tested this with Oak and Birch doors, but it should be the same for all the other ones, too.