A critical challenge in temporal planning is robustly dealing with non-determinism introduced by the environment, e.g., the durational uncertainty of an action taken by a robot in the physical world due to slippage or other unexpected influences. Recent advances show that robustness, which accounts for uncertainty in predicting schedule success, is a better measure of solution quality than traditional metrics such as flexibility. This paper introduces the Robust Execution Problem (REP) for finding maximally robust dispatch strategies for general probabilistic temporal planning problems. While the REP is generally intractable in practice, we introduce approximate solution techniques—one that can be computed statically prior to the start of execution while providing robustness guarantees and one that dynamically adjusts to opportunities and setbacks during execution. We show empirically that dynamically optimizing for robustness improves the likelihood of execution success.