Code completion is a key feature of Integrated Development Environments (IDEs), aimed at predicting the next tokens a developer is likely to write, helping them write code faster and with less effort. Modern code completion approaches are often powered by deep learning (DL) models. However, the swift evolution of programming languages poses a critical challenge to the performance of DL-based code completion models: Can these models generalize across different language versions? This paper delves into such a question. In particular, we assess the capabilities of a state-of-the-art model, CodeT5, to generalize across nine different Java versions, ranging from Java 2 to Java 17, while being exclusively trained on Java 8 code. Our evaluation spans three completion scenarios, namely, predicting tokens, constructs (e.g., the condition of an if statement) and entire code blocks. The results of our study reveal a noticeable disparity among language versions, with the worst performance being obtained in Java 2 and 17 - the most far apart versions compared to Java 8. We investigate possible causes for the performance degradation and show that the adoption of a limited version-specific fine-tuning can partially alleviate the problem. Our work raises awareness on the importance of continuous model refinement, and it can inform the design of alternatives to make code completion models more robust to language evolution.