Sickness
From PinataIsland.info, the Viva Piñata wiki
Pinatas in the Xbox 360 game never die. If you hit pinata with the shovel they can become ill, or even break open. Even when broken open, they will reappear at the outside edge of your garden.
However a pinata can get sick. Should your pinata get sick you can choose to ignore the pinatas ailment or you can try to cure it. Should a pinata get too sick to heal it will leave your garden and return to the wild. It will also discard any accessories you have put on it.
