In portable mobile communications, variable complexity Fano decoders are of interest because they offer a desirable tradeoff between bit error rate (BER) and decoding complexity. The practical use of Fano decoders is made possible by buffers that are able to absorb the variations in decoding delays. The optimal buffer control scheme aims to minimize the overall probability of block loss, which is comprised of the loss due to excessive bit errors caused by fast yet coarse decoding, and the loss due to buffer overflow caused by long processing delays. While our previous work has yielded a solution to the control problem over memoryless channel, we now investigate Fano decoding over channels with memory. We seek to achieve better control performance by taking advantage of the memory of the channel. We use slow, flat Rayleigh fading channels as an example to demonstrate that prediction based on two-state Markov models can further lower the probability of block loss.