When you add cycles, tracing the chain of arrows back does not need to end at anything you find remotely satisfactory or even unique - "the ball moved because it hit itself because it moved because it hit itself..."

This is a problem with your personal intuitions as a medium-sized multicellular century-lived mammalian tetrapod. No event in this chain is left uncaused, and there are no causes which lack effects in this model. Causality is satisfied. If you are not, that's your problem. Hell, the energy is even conserved. It runs in a spatial as well as a temporal circle, what with the ball hitting itself and skidding to a stop exactly where it was sitting to wait for the next hit. On the other hand, in such a universe quantum mechanics does not apply, because worldlines cannot split, which also removes any possibility of entropy. ALL interactions are 100% efficient.