Postural stabilization during rapid and powerful hopping actions represents a significant challenge for legged robotics. One strategy utilized by humans to negotiate this difficulty is the robust activation of biarticular thigh muscles. Guided by this physiological principle, this study aims to enhance the postural stability of a hopping robot through the emulation of this human mechanism. A legged robot powered by pneumatic artificial muscles (PAMs) was designed to mimic human anatomical structures. A critical aspect of this development was creating a tension-oriented stretch reflex system engineered to initiate muscle activation in response to perturbations. Our research encompassed three experiments: 1) assessing the trunk pitch angle with and without the integration of stretch reflexes, 2) evaluating the consistency of hops made with and without reflexes, and 3) understanding the correlation between the reflex strength equilibrium in the biarticular thigh muscles and trunk pitch angle. The results indicated that the integration of the stretch reflex minimized perturbations, thereby allowing the robot to perform double the continuous hops. As hypothesized, adjusting the reflex strength equilibrium caused a shift in the angle. This reflex mechanism offers potential application to PAM-driven robots and signifies a promising avenue for enhancing postural stability in diverse forms of locomotion, including walking and running.