We examine the effects of time dilation on the temporal profiles of gamma-ray burst (GRB) pulses. By using prescriptions for the shape and evolution of prompt gamma-ray spectra, we can generate a simulated population of single-pulsed GRBs at a variety of redshifts and observe how their light curves would appear to a gamma-ray detector here on Earth. We find that the observer frame duration of individual pulses does not increase with redshift as 1 + z, which one would expect from cosmological expansion. This time dilation is masked by an opposite and often stronger effect: with increasing redshift and decreasing signal-to-noise ratio only the brightest portion of the light curve can be detected. The results of our simulation are consistent with the fact that the simple time dilation of GRB light curves has not materialized in either the Swift or Fermi detected GRBs with known redshift. We show that the measured durations and associated E sub(iso) estimates for GRBs detected near the instrument's detection threshold should be considered lower limits to the true values. Furthermore, we conclude that attempts at distinguishing between long and short GRBs, at even moderate redshifts, cannot be done based on a burst's temporal properties alone.