  Current test-time adaptation (TTA) approaches aim to adapt to environments
that change continuously. Yet, when the environments not only change but also
recur in a correlated manner over time, such as in the case of day-night
surveillance cameras, it is unclear whether the adaptability of these methods
is sustained after a long run. This study aims to examine the error
accumulation of TTA models when they are repeatedly exposed to previous testing
environments, proposing a novel testing setting called episodic TTA. To study
this phenomenon, we design a simulation of TTA process on a simple yet
representative $\epsilon$-perturbed Gaussian Mixture Model Classifier and
derive the theoretical findings revealing the dataset- and algorithm-dependent
factors that contribute to the gradual degeneration of TTA methods through
time. Our investigation has led us to propose a method, named persistent TTA
(PeTTA). PeTTA senses the model divergence towards a collapsing and adjusts the
adaptation strategy of TTA, striking a balance between two primary objectives:
adaptation and preventing model collapse. The stability of PeTTA in the face of
episodic TTA scenarios has been demonstrated through a set of comprehensive
experiments on various benchmarks.
