I have tried reinstalling the game and un-equiping the items and using larger potion sizes all the way to power elixer's. Please post any suggestions for me to try!
It only auto heals when you reach a certain % of HP/MP (That % can be changed in your game settings).
If the pet is alive and you have potions in the slots (in your equip screen) and it isn't working, try doing a clean reboot.
Sometimes if you're running the client in Windows. Make sure it's checked on Windows box. If full screen, checked full screen. I had this issue last time. All I did was that. Hope it helps