My pets almost always came back for extra lives. In addition to food and other health considerations, your pets need love and play. Are you spending very much time playing with your pets and grooming them? Are you accidentally hitting them? If you're careful to play with your pet frequently (I usually play with them until they get tired and fall asleep) and do other things that they like (different pets like different things), they will love you and want to come back after they die.