Collections of motors dynamically organize to extract membrane tubes. These tubes grow but often pause or change direction as they traverse an underlying microtubule (MT) network. In vitro, membrane tubes also stall: they stop growing in length despite a large group of motors available at the tip to pull them forward. In these stationary membrane tubes in vitro, we find that clusters of processive kinesin motors form and reach the tip of the tube at regular time intervals. The average times between cluster arrivals depends on the time over which motors depart from the tip, suggesting that motors are recycled toward the tip. Numerical simulations of the motor dynamics in the membrane tube and on the MTs show that the presence of cooperative binding between motors quantitatively accounts for the clustering observed experimentally. Cooperative binding along the length of the MT and a nucleation point at a distance behind the tip define the recycling period. Based on comparison of the numerical results and experimental data, we estimate a cooperative binding probability and concentration regime where the recycling phenomenon occurs.