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We study the onset of microreversibility in simulations of cyclically sheared soft-sphere systems. In particular, we focus on the transition from point-like reversibility in which there are no particle collisions over a shear cycle to loop-like reversibility in which there are particle collisions. We find that the transition from point- to loop-like reversibility shifts from phi_J, the onset of jamming, to phi_P, the onset of contact percolation, as the strain amplitude increases from 0 to \infty. We study cluster-size distributions, breaking and reformation of contacts, and non-affine motion in the vicinity of this reversibility transition.
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