The answer is the Heart (thank goodness).
Although the other organs listed either operate on a 24-hour clock or by other influences, they also technically never completely rest. The kidneys are under the influence of hydrostatic force from our blood pressure (the heart) which as we stated is constant, but they will slow down their activity and rest. The liver will also exhibit circadian rhythms to its functions and can rest depending on the need for metabolic activity. Your digestive system and the stomach continue to work even while you are asleep, however, it significantly slows down while we are not eating or drinking during this time and therefore is also allowed to rest. It is thought that these diurnal resting periods aid in maintaining the homeostasis of the various organs and systems of the body.
Although the force of contraction in the heart may fluctuate, the intrinsic nervous stimulation to the myocardium continues while we are awake or sleeping around the clock, making the heart the best answer to the question.
