In this paper, the problem of lossy source coding with side information at the decoder is considered when the dependency between the source and the side information (SI) is quasi-stationary and unknown to the encoder. This dependency is modeled using a (virtual) block fading channel. In order to help the decoder estimate the dependency, a part of the transmitted source in each block is coded at high rate (disregarding the SI) to be decoded error-free at the decoder. The estimate of the virtual block fading channel is imperfect and its quality depends on the length of the estimation block. The decoder's estimate is then quantized and communicated back to the encoder using a limited rate feedback. The encoder encodes the rest of the source block with this knowledge of the SI dependency model. A source coding scheme that uses the estimated dependency structure is proposed and the appropriate length of the source assigned for the estimation phase is characterized so as to minimize the mean distortion. The effect of the feedback rate, the quantization step size and the dependency estimation error are also investigated.