In frustrated spinel antiferromagnets, dilution with non-magnetic ions can be a powerful strategy for probing unconventional spin states or uncovering interesting phenomena. Here, we present X-ray, neutron scattering and thermodynamic studies of the effects of magnetic dilution of the tetragonally-distorted A-site spinel antiferromagnet, CuRh2O4, with non-magnetic Zn 2+ ions. Our data confirm the helical spin order recently identified at low-temperatures in this material, and further demonstrate a systematic suppression of the associated Néel temperature with increasing site dilution towards a continuous transition with critical doping of xspin ∼ 0.44. Interestingly, this critical doping is demonstrably distinct from a second structural critical point at xJT ∼ 0.6, which is consistent with the suppression of orbital order on the A-site through a classical percolative mechanism. This anomalously low value for xspin is confirmed via multiple measurements, and is inconsistent with predictions of classical percolation theory, suggesting that the spin transition in this material is driven by an enhancement of pre-existing spin fluctuations with weak dilution.