We investigate the existence of chiral zero modes at a(-1) similar or equal
to 1 GeV in quenched domain-wall QCD. Simulations are carried out for the
plaquette and an RG-improved gauge actions on a 12(3) x 24 x N-s lattice wi
th N-s = 10 - 50. We find that the pion mass in the chiral limit remains no
n-vanishing as N-s --> infinity for both gauge actions. Possible origins of
this non-vanishing pion mass are discussed.