  Electron transport in a disordered graphene nanoribbon with zigzag edges is
crucially affected by a perfectly conducting channel (PCC), which is stabilized
if intervalley scattering is ignorable. In the presence of such a PCC, the
dimensionless conductance g of the system decreases to the quantized value of g
= 1 with increasing system length L. In the realistic case where intervalley
scattering is weak but not ignorable, the PCC is gradually destabilized with
increasing L, and g eventually decays to zero owing to the onset of Anderson
localization. Here, we show that such destabilization of the PCC can be relaxed
by pure dephasing. We numerically calculate g in the presence of long-range
impurities, which induce weak intervalley scattering, taking the dephasing
effect into account. It is demonstrated that, under sufficient dephasing, the
decay of g in the regime of g \lesssim 1 is strongly suppressed and the
quasi-quantization of g (i.e., g ~ 1) can be observed in a wide region of L.
