Slimes, magma cubes, and ender dragons (charge attack) can hit every tick, meaning they can break your shield in seconds.

Steps to reproduce:
Method 1:

1. Trap a large or medium slime, or a magma cube of any size, in a small area with walls and a roof so that it cannot jump to full height or be knocked back by the shield the full distance it normally would be.
2. Enter the area while holding a shield. (See Shield breaker.mp4.)

Method 2:

1. Trap a large or medium slime, or a magma cube of any size, in a minecart.
2. Use a shield while walking into the minecart. (See Shield breaker 2.mp4.)

Method 3:

1. Use a shield while the ender dragon charges at you. (See Shield breaker 3.mp4.)

Expected Results:
Slimes, magma cubes, and the ender dragon attack the same number of times per second as other melee attack mobs.

Observed Results:
These attacks have no attack/damage cooldown. The shield blocks the attack so many times per second that it breaks even with full durability.