Pure Edge computing (PEC) aims to bring cloud applications and services to the edge of the network to support the growing user demand for time-sensitive applications and data-driven computing. However, mobility and limited computational capacity of edge devices pose challenges in supporting some urgent and computationally intensive tasks with strict response time demands. If the execution results of these tasks exceed the deadline, they become worthless and can cause severe safety issues. Therefore, it is essential to ensure that edge nodes complete as many latency-sensitive tasks as possible. \\In this paper, we propose a Robust Adaptive Workload Orchestration (R-AdWOrch) model to minimize deadline misses and data loss by using priority definition and a reallocation strategy. The results show that R-AdWOrch can minimize deadline misses of urgent tasks while minimizing the data loss of lower priority tasks under all conditions.