An unusual, non-metallic resistivity of the 111 iron-pnictide compound FeCrAs is shown to be relatively unchanged under pressures of up to 17 GPa. Combined with our previous finding that this non-metallic behaviour persists from at least 80 mK to 800 K, this shows that the non-metallic phase is exceptionally robust. Antiferromagnetic order, with a Neel temperature T_N ~ 125 K at ambient pressure, is suppressed at a rate of 7.1 +/- 0.1 K/GPa, falling to below 50 K at 10 GPa. We conclude that formation of a spin-density wave gap at T_N does not play an important role in the non-metallic resistivity of FeCrAs at low temperatures.