There is resistance when you stretch a rubber band. That makes sense to me because the energy you exert is turned into potential energy of the rubber band, but if you hold the rubber band in the same stretched position, it requires constant energy from your body to keep it stretched, but the rubber band doesn't gain any extra potential energy. Where does that energy go?
Holding a rubber band stretched is the same as holding a weight above the ground. You aren't adding any energy to the weight, just maintaining its position. However, your muscles' actin and myosin require energy input just to maintain a force. This energy ends up heating the muscles, and is lost.