Maintenance in small hydroelectric plants (SHPs) is essential for securing the expansion of clean energy sources and supplying the energy estimated to be required for the coming years. Identifying failures in SHPs before they happen is crucial for allowing better management of asset maintenance, lowering operating costs, and enabling the expansion of renewable energy sources. Most fault prognosis models proposed thus far for hydroelectric generating units are based on signal decomposition and regression models. In the specific case of SHPs, there is a high occurrence of data being censored, since the operation is not consistently steady and can be repeatedly interrupted due to transmission problems or scarcity of water resources. To overcome this, we propose a two-step, data-driven framework for SHP prognosis based on time series feature engineering and survival modeling. We compared two different strategies for feature engineering: one using higher-order statistics and the other using the Tsfresh algorithm. We adjusted three machine learning survival models—CoxNet, survival random forests, and gradient boosting survival analysis—for estimating the concordance index of these approaches. The best model presented a significant concordance index of 77.44%. We further investigated and discussed the importance of the monitored sensors and the feature extraction aggregations. The kurtosis and variance were the most relevant aggregations in the higher-order statistics domain, while the fast Fourier transform and continuous wavelet transform were the most frequent transformations when using Tsfresh. The most important sensors were related to the temperature at several points, such as the bearing generator, oil hydraulic unit, and turbine radial bushing.