A numerical analysis based on the nonlinear Schroedinger equation is presented to analyze the propagation stability of the average soliton in a simple nonlinear amplifying loop mirror. The ratio of amplification period to soliton period and the length fraction of the erbium-doped fiber in the loop are varied to investigate their effects on the soliton stability. It is observed that stable soliton propagation is obtained even when the amplification period is only slightly shorter than the soliton period when the length fraction of the erbium-doped fiber in the loop is small, which is different from the previously published condition for stable average soliton propagation.