All pets have 100 Health regardless of their level, though this is balanced because no matter what type of attack or the attack value of the enemy your pet can only take 1 damage per hit. If your pet health reaches zero, your pet will die. A dead pet becomes sealed and cannot be summoned or re-equipped until it is unsealed. Go see the animal trainer and click "Unseal your Pet." Then with your inventory on screen, drag your pet icon to the window and it tells you also how much to "Unseal or Revive" your pet.

If you fail to heal your pet regularly, it can affect your pet's sympathy with your character and thus decrease the effectiveness of the pet's skills.