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Robot planning in distributed systems, such as drone fleets performing active perception missions, presents complex challenges. These missions require cooperation to achieve objectives like collecting sensor data or capturing images. Multi-robot systems offer significant advantages, including faster execution and increased robustness, as robots can compensate for individual failures. However, resource costs, affected by environmental factors such as wind or terrain, are highly uncertain, impacting battery consumption and overall performance. Mission objectives are often prioritized by criticality, such as retrieving data from low-battery sensors to prevent data loss. Addressing these priorities requires sophisticated scheduling to navigate high-dimensional state-action spaces. While heuristics are useful for approximating solutions, few approaches extend to multi-robot systems or adequately address cost uncertainty and criticality, particularly during replanning. The Mixed-Criticality (MC) paradigm, extensively studied in real-time scheduling, provides a framework for handling cost uncertainty by ensuring the completion of high-critical tasks. Despite its potential, the application of MC in distributed systems remains limited. To address the decision-making challenges faced by distributed robots operating under cost uncertainty and objective criticality, we propose four contributions: a comprehensive model integrating criticality, uncertainty, and robustness; distributed synchronization and replanning mechanisms; the incorporation of mixed-criticality principles into multi-robot systems; and enhanced resilience against robot failures. We evaluated our solution, named RESCUE, in a simulated scenario and show how it increases the robustness by reducing the oversizing of the system and completing up to 40% more objectives. We found an increase in resilience of the multi-robot system as our solution not only guaranteed the safe return of every non-faulty robot, but also reduced the effects of a faulty robot by up to 14%. We also computed the performance gain compared to using MCTS in a single robot of up to 2.31 for 5 robots.