Low-power wireless networks have the potential to enable applications that are of great importance to industry and society. However, existing network protocols do not meet the dependability requirements of many scenarios as the failure of a single node or link can completely disrupt communication and take significant time and energy to recover. This paper presents Hydra, a low-power wireless protocol that guarantees robust communication despite arbitrary node and link failures. Unlike most existing deterministic protocols, Hydra steers clear of centralized coordination to avoid a single point of failure. Instead, all nodes are equivalent in terms of protocol logic and configuration, performing coordination tasks such as synchronization and scheduling concurrently. This concept of concurrent coordination relies on a novel distributed consensus algorithm that yields provably unique decisions with low delay and energy overhead. In addition to a theoretical analysis, we evaluate Hydra in a multi-hop network of 23 nodes. Our experiments demonstrate that Hydra withstands random node failures without increasing coordination overhead and that it re-establishes efficient and reliable data exchange within seconds after a major disruption.