In this paper, we study the robustness of scheduling against channel variations. Specifically, we consider a class of generalized proportional fairness (PF) schedulers that achieve optimal throughput-fairness trade-off and study their robustness in terms of maintaining a certain fairness criterion when the channel statistics change from the additive white Gaussian noise (AWGN) to Rayleigh fading for all users. We conclude that the scheduler is robust only when it is configured to achieve the proportional fairness. For the other scheduler configurations, which are not robust, we show how fairness deviates from the ideal one when the channel statistics change and show how scheduler parameters need to be adjusted to restore the desired fairness. We also show simulation results.