Deep recommendation systems (DRS) heavily depend on specialized HPC hardware and accelerators to optimize energy, efficiency, and recommendation quality. Despite the growing number of hardware errors observed in large-scale fleet systems where DRS are deployed, the robustness of DRS has been largely overlooked. This paper presents the first systematic study of DRS robustness against hardware errors. We develop Terrorch, a user-friendly, efficient and flexible error injection framework on top of the widely-used PyTorch. We evaluate a wide range of models and datasets and observe that the DRS robustness against hardware errors is influenced by various factors from model parameters to input characteristics. We also explore 3 error mitigation methods including algorithm based fault tolerance (ABFT), activation clipping and selective bit protection (SBP). We find that applying activation clipping can recover up to 30% of the degraded AUC-ROC score, making it a promising mitigation method.