Partial-order plans (POPs) have the capacity to compactly represent numerous distinct plan linearizations and as a consequence are inherently robust. We exploit this robustness to do effective execution monitoring. We characterize the conditions under which a POP remains viable as the regression of the goal through the structure of a POP. We then develop a method for POP execution monitoring via a structured policy, expressed as an ordered algebraic decision diagram. The policy encompasses both state evaluation and action selection, enabling an agent to seamlessly switch between POP linearizations to accommodate unexpected changes during execution. We demonstrate the effectiveness of our approach by comparing it empirically and analytically to a standard technique for execution monitoring of sequential plans. On standard benchmark planning domains, our approach is 2 to 17 times faster and up to 2.5 times more robust than comparable monitoring of a sequential plan. On POPs that have few ordering constraints among actions, our approach is significantly more robust, with the ability to continue executing in up to an exponential number of additional states.