Nowadays, smart mobile devices generate huge amounts of data in all sorts of gatherings. Much of that data has localized and ephemeral interest, but can be of great use if shared among co-located devices. However, these devices often experience poor connectivity, leading to availability issues if applications' storage and logic are fully delegated to a remote cloud infrastructure. In turn, the edge computing paradigm pushes computations and storage beyond the data center, closer to end-user devices where data is generated and consumed. Thus, enabling the execution of certain components of edge-enabled systems directly and cooperatively on edge devices. In this paper, we address the challenge of supporting reliable and efficient data storage and dissemination among co-located wireless mobile devices without resorting to centralized services or network infrastructures. We propose Thyme, a novel time-aware reactive data storage system for wireless edge networks, that exploits synergies between the storage substrate and the publish/subscribe paradigm. We present the design of Thyme and evaluate it through simulation, characterizing the scenarios best suited for its use. The evaluation shows that Thyme allows for reliable notification and retrieval of relevant data with low overhead and latency.