We analyze the asymptotic behavior of the cross-polarized enhancement factor in the framework of the standard low-packing-density theory of coherent backscattering by discrete random media composed of spherically symmetric particles. It is shown that if the particles are strongly absorbing or if the smallest optical dimension of the particulate medium (i.e., the optical thickness of a plane-parallel slab or the optical diameter of a spherically symmetric volume) approaches zero, then the cross-polarized enhancement factor tends to its upper-limit value 2. This theoretical prediction is illustrated using direct computer solutions of the Maxwell equations for spherical volumes of discrete random medium.