The dynamics of vibro-impact systems near grazing is known to be singular. The authors have recently exhibited nonlinear modal motions in the vicinity of grazing orbits within a conservative framework, suggesting the latter play a important role in the dynamics. In this work, insights on the dynamics of solutions near some periodic grazing orbits are given. It is found that the first return time may involve a square-root singularity or a cube-root singularity and also become discontinuous. These properties may affect the first return map and thus the dynamics near grazing orbits.