The highly temporal variability of the hydrological response in Mediterranean areas affects the operation of hydropower systems, especially in run-of-river (RoR) plants located in mountainous areas. Here, the water flow regime strongly determines failure, defined as no operating days due to inflows below the minimum operating flow. A Bayesian dynamics stochastic model was developed with statistical modeling of both rainfall as the forcing agent and water inflows to the plants as the dependent variable using two approaches—parametric adjustments and non-parametric methods. Failure frequency analysis and its related operationality, along with their uncertainty associated with different time scales, were performed through 250 Monte Carlo stochastic replications of a 20-year period of daily rainfall. Finally, a scenario analysis was performed, including the effects of 3 and 30 days of water storage in a plant loading chamber to minimize the plant’s dependence on the river’s flow. The approach was applied to a mini-hydropower RoR plant in Poqueira (Southern Spain), located in a semi-arid Mediterranean alpine area. The results reveal that the influence of snow had greater operationality in the spring months when snowmelt was outstanding, with a 25% probability of having fewer than 2 days of failure in May and April, as opposed to 12 days in the winter months. Moreover, the effect of water storage was greater between June and November, when rainfall events are scarce, and snowmelt has almost finished with operationality levels of 0.04–0.74 for 15 days of failure without storage, which increased to 0.1–0.87 with 3 days of storage. The methodology proposed constitutes a simple and useful tool to assess uncertainty in the operationality of RoR plants in Mediterranean mountainous areas where rainfall constitutes the main source of uncertainty in river flows.