Advanced reactor designers are looking to maximize the system capacity factor to make advanced reactors more economically competitive and meet the projected energy demand. To achieve this goal, we propose a Dynamic Operation and Maintenance Optimization (DyOMO) framework to perform system-level predictive maintenance (PdM) using a dynamic Bayesian network and component-specific PdM using deep neural networks. At the system level, DyOMO detects the presence of anomalous phenomena, determines the most influential degradation mode, and estimates the remaining useful life (RUL) distribution for the system. At the component level, DyOMO summarizes the health state of key system components, determines the presence of an anomaly using a feedforward neural network, and predicts component RUL using a Bayesian neural network. To evaluate the overall performance of DyOMO, normal operations of a Pebble-Bed High-Temperature Gas-cooled Reactor (PB-HTGR) were simulated with realistic component degradation for the steam turbine and steam generator. Across the 20 independent reactor life simulations, it was found that maintenance was always performed before any safety limits were violated and before a component failed. Specifically, the system-level PdM suggested maintenance on the steam generator once the steam pressure approached its safety limit, and the component-specific PdM suggested maintenance on the steam turbine once the turbine blade hardness degraded. The results indicate that through the continuous monitoring of the system and individual components, the DyOMO framework improves safety and increases the availability of the reactor when compared to traditional maintenance philosophies.