We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. Both the defender and the intruders have non-holonomic dynamics. The intruders' objective is to breach the target perimeter without being captured by the defender, while the defender's goal is to capture as many intruders as possible. After one intruder breaches or is captured, the next appears randomly on a fixed circle surrounding the target. Therefore, the defender's final position in one game becomes its starting position for the next. We divide an intruder-defender engagement into two phases, partial information and full information, depending on the information available to the players. We address the capturability of an intruder by the defender using the notions of Dubins path and guarding arc. We quantify the percentage of capture for both finite and infinite sequences of incoming intruders. Finally, the theoretical results are verified through numerical examples using Monte-Carlo-type random trials of experiments.