  We show that near-infrared observations of the red side of the Ly-alpha line
from a single gamma ray burst (GRB) afterglow cannot be used to constrain the
global neutral fraction of the intergalactic medium (IGM), x_H, at the GRB's
redshift to better than ~0.3. Some GRB sight-lines will encounter more neutral
hydrogen than others at fixed x_H owing to the patchiness of reionisation. GRBs
during the epoch of reionization will often bear no discernible signature of a
neutral IGM in their afterglow spectra. We discuss the constraints on x_H from
the z = 6.3 burst, GRB050904, and quantify the probability of detecting a
neutral IGM using future spectroscopic observations of high-redshift,
near-infrared GRB afterglows. Assuming an observation with signal-to-noise
similar to the Subaru FOCAS spectrum of GRB050904 and that the column density
distribution of damped Ly-alpha absorbers is the same as measured at lower
redshifts, a GRB from an epoch when x_H = 0.5 can be used to detect a partly
neutral IGM at 98% confidence level 10% of the time (and, for an observation
with three times the sensitivity, 30% of the time).
