We report evidence that the asymptotic low-energy power-law slope ct (below the spectral break) of BATSE gamma-ray burst (GRB) photon spectra evolves with time rather than remaining constant. We find that a high degree of positive correlation exists between the time-resolved spectral break energy E(pk) and alpha. In samples of 18 ''hard-to-soft'' and 12 ''tracking'' pulses, evolution of alpha was found to correlate with that of the spectral break energy E(pk) at the 99.7% and 98% confidence levels, respectively. We also find that in the flux rise phase of hard-to-soft pulses, the mean value of alpha is often positive, and in some bursts the maximum value of alpha is consistent with a value > +1. BATSE burst 3B 910927, for example, has an alpha(max) equal to 1.6 +/- 0.3. These findings challenge GRB spectral models in which alpha must be negative or remain constant.