Deep learning (DL) models have been deployed in various platforms, including resource-constrained environments such as edge computing, smartphones, and personal devices. Such deployment requires models to have smaller sizes and memory footprints. To this end, many model compression techniques proposed in the literature successfully reduce model sizes and maintain comparable accuracy. However, the robustness of compressed DL models against class imbalance, a natural phenomenon in real-life datasets, is still under-explored. We present a comprehensive experimental study of the performance and robustness of compressed DL models when trained on class-imbalanced datasets. We investigate the robustness of compressed DL models using three popular compression techniques (pruning, quantization, and knowledge distillation) with class-imbalanced variants of the CIFAR-10 dataset and show that compressed DL models are not robust against class imbalance in training datasets. We also show that different compression techniques have varying degrees of impact on the robustness of compressed DL models.