In this work, we investigate the problem of bit-rate adaptation transcoding for transmitting video over burst-error wireless channels, i.e., channels such that errors tend to occur in clusters during fading periods. In particular, we consider a scenario consisting of packet-based transmission with an Automatic Repeat reQuest (ARQ) error control and a feedback channel. With the acknowledgements received through the feedback channel and a statistical channel model, we have an estimate of the current channel state, and effective channel bandwidth. In this paper, we analyze the buffering implications of inserting a video transcoder at the wireless access point with the variable bit-rate channel as the target. We derive the conditions that both the source encoder and transcoder buffers have to meet for preventing the end decoder buffer from underflowing. Furthermore, we propose a bit-rate adaptation algorithm for VBR transcoders used in the wireless access point. Our experimental results demonstrate that the proposed algorithm can accurately control the bit-rate of the transcoded video stream and reduce the number of frames been skipped without violating the end-to-end delay requirement.