Deep learning (DL), a form of machine learning, is becoming increasingly popular in several application domains. As a result, cloud-based Deep Learning as a Service (DLaaS) platforms have become an essential infrastructure in many organizations. These systems accept, schedule, manage and execute DL training jobs at scale. This paper explores dependability in the context of a DLaaS platform used in IBM. We begin by explaining how DL training workloads are different, and what features ensure dependability in this context. We then describe the architecture, design and implementation of a cloud-based orchestration system for DL training. We show how this system has been architected with dependability in mind while also being horizontally scalable, elastic, flexible and efficient. We also present an initial empirical evaluation of the overheads introduced by our platform, and discuss tradeoffs between efficiency and dependability.