The perturbation response of muscle is important for the versatile, stable and agile control capabilities of animals. Muscle resists being stretched by developing forces in the passive tissues and in the active crossbridges. This review focuses on the active perturbation response of the sarcomere. The active response exhibits typical stress relaxation, and thus approximated by a Maxwell material that has a spring and dashpot arranged in series. The ratio of damping to stiffness in this approximation defines the relaxation timescale for dissipating stresses that are developed in the crossbridges due to external perturbations. Current understanding of sarcomeres suggests that stiffness varies nearly linearly with neural excitation, but not much is known about damping. But if both stiffness and damping have the same functional (linear or not) dependence on neural excitation, then the stress relaxation timescale cannot be varied depending on the demands of the task. This implies an unavoidable and biologically unrealistic trade-off between how freely the crossbridges can yield and dissipate stresses when stretched (injury avoidance in agile motions) vs. how long they can maintain perturbation-induced stresses and behave like a solid material (stiffness maintenance for stability). We hypothesize that muscle circumvents this trade-off by varying damping in a nonlinear manner with neural excitation, unlike stiffness that varies linearly. Testing this hypothesis requires new experimental and mathematical characterization of muscle mechanics, and also identifies new design goals for robotic actuators.