I believe Elytra were exempt from this, allowing you to repair them using Leather as many times as you wanted, because of their rarity in comparison to normal tools or armor. This is also the reason Elytra don't disappear when they lose all their durability.
Elytra can Become "Too Expensive" to Repair at Anvils
So, 15w42a was released today, and it looks like that Jeb and Mojang have decided on a new system. The Mending enchantment was introduced. An item with this enchantment will have its durability restored, if needed, as the player collects experience. Exp. goes to the mendable item instead of the player. Therefore, elytra can be infinitely repaired if it has Mending. However, enchanted books with Mending will only be found in the world, like elytra. Locations haven't been implemented nor confirmed at this time.
The not breaking/disappearing when losing all durability has been present since they were introduced I believe and was probably added because they are much more valuable than other items.
You can only repair any item just 6 times on the anvil before it becomes too expensive; anybody would rather use Mending instead so you don't even need any materials (though I think it should work like renaming did before 1.8, making you have to use materials to repair items on the anvil along with the repair costs depending on the item and enchantments):
After six workings, the penalty will be 63 levels, making any further repair or enchantment impossible in survival.