Butlers don't have the full set of needs as regular Sims; all they really need is Sleep, Fun, and Hunger. A butler only goes away if you intend to dismiss their services and no longer need them, so unless you no longer want your butler, they will continue to hang around your home. Technically, butlers don't really need you to provide them a bed, I haven't seen it with any of mine but if they become too tired they may leave the lot for some time and come back eventually, though it is much nicer to provide your butler with a nice bed! :)