Machine learning-based performance models are increasingly being used to build critical job scheduling and application optimization decisions. Traditionally, these models assume that data distribution does not change as more samples are collected over time. However, owing to the complexity and heterogeneity of production HPC systems, they are susceptible to hardware degradation, replacement, and/or software patches, which can lead to drift in the data distribution that can adversely affect the performance models. To this end, we develop continually learning performance models that account for the distribution drift, alleviate catastrophic forgetting, and improve generalizability. Our best model was able to retain accuracy, regardless of having to learn the new distribution of data inflicted by system changes, while demonstrating a 2X improvement in the prediction accuracy of the whole data sequence in comparison to the naive approach.