Are you using it correctly?
First: double-click on the skill to make the pet learn it.
Then: assign a potion to the skill by dragging it from your Use inventory to the appropriate slot in the PET tab of your Equipment window.
Note that the pet will only use one potion when your HP drops below the threshold defined in your game options. If that fails to bring your HP above the threshold, the pet will not use another potion. Which means that if you are fighting enemies that hit for, say, 1000 HP at a time, putting a 300 HP potion on your auto-HP slot is not going to save you from dying.