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Identifying and mitigating bias in deep learning algorithms has gained significant popularity in the past few years due to its impact on the society. Researchers argue that models trained on balanced datasets with good representation provide equal and unbiased performance across subgroups. However, can seemingly unbiased pre-trained model become biased when input data undergoes certain distortions? For the first time, we attempt to answer this question in the context of face recognition. We provide a systematic analysis to evaluate the performance of four state-of-the-art deep face recognition models in the presence of image distortions across different gender and race subgroups. We have observed that image distortions have a relationship with the performance gap of the model across different subgroups.