A pet's Love decreases by 1 per hour. When it gets to 0 or below, the pet whines at you, and the increase of Esteem and experience points becomes impossible.
A sleeping pet does not lose any Love.
As a pet feels less loved, it is more likely to spend its hourly action being comforted by love items in the house (plushies, for example).
Many foods provide Love when fed to a pet, and most half-hourly actions - including petting - provide Love, when taken.