We have measured the azimuthal anisotropy of p⁰ production for 1<p_T<18 GeV/c for Au+Au collisions at Ö^s_NN=200 GeV. The observed anisotropy shows a gradual decrease for 3 £ p_T £ 7–10 GeV/c, but remains positive beyond 10 GeV/c. The magnitude of this anisotropy is underpredicted, up to at least ~10 GeV/c, by current perturbative QCD (PQCD) energy-loss model calculations. An estimate of the increase in anisotropy expected from initial-geometry modification due to gluon saturation effects and fluctuations is insufficient to account for this discrepancy. Calculations that implement a path-length dependence steeper than what is implied by current PQCD energy-loss models show reasonable agreement with the data.