human biology - Why is the Patellar reflex not triggered when the tendon is extended slowly?

This effect you are observing has to do with the nature of the afferent neurons (Ia fibers), which carry a signal into the spinal cord and synapse onto motor neurons directly. See this text (scroll down to section 1.10) for a diagram. At their other end, these Ia fibers penetrate into the muscle and wrap themselves around the body of the muscle spindles, "[which] are specialized receptors that signal (a) the length and (b) the rate of change of length (velocity) of the muscle."

Because the main role of these spindles is to monitor the muscles for very rapid changes in length, the neurons have a static range which is optimized for these quick jerks (rather than firing over a wide range of velocities). When you are stretching the muscle slowly, the Ia fiber is not building up a sufficient depolarization to fire off an action potential.