Abstract: Current test-time adaptation (TTA) approaches aim to adapt to environments that change continuously. Yet, it is unclear whether TTA methods can maintain their adaptability over prolonged periods. To answer this question, we introduce a diagnostic setting - **recurring TTA** where environments not only change but also recur over time, creating an extensive data stream. This setting allows us to examine the error accumulation of TTA models, in the most basic scenario, when they are regularly exposed to previous testing environments. Furthermore, we simulate a TTA process on a simple yet representative $\epsilon$-**perturbed Gaussian Mixture Model Classifier**, deriving theoretical insights into the dataset- and algorithm-dependent factors contributing to gradual performance degradation. Our investigation leads us to propose **persistent TTA (PeTTA)**, which senses when the model is diverging towards collapse and adjusts the adaptation strategy, striking a balance between the dual objectives of adaptation and model collapse prevention. The supreme stability of PeTTA over existing approaches, in the face of lifelong TTA scenarios, has been demonstrated over comprehensive experiments on various benchmarks.