Instabilities of long-range order are observed in samples of the d = 3 dilute uniaxial antiferromagnet Fe xZn1-xF2 with x = 0:56 and 0.41, under strong random fields. The onset of instability, mapped in the (H, T) phase diagrams of the samples, reveals that the H, T and x dependence of the effective random field is in qualitative agreement with a mean-field expression predicted in the weak-field limit for site diluted antiferromagnets.