Existing motion forecasting models, while making progress, struggle to bridge the gap between the source and target domains. Recent solutions often rely on an unrealistic assumption that the target domain remains stationary. Due to the ever-changing environment, however, the real-world test distribution may experience ongoing/continual shifts over time, leading to catastrophic forgetting and error accumulation when adapting to evolving domains. To solve these challenges, this work introduces HoCoTTA, a framework for homeostatic continual test-time adaptation. It aligns with the knowledge distillation and parameter isolation paradigm, enabling the identification of domain-invariant and domain-specific knowledge, where the former is shared (to be retained) in continual TTA across domains, while the latter needs to be updated. Specifically, we propose a multi-domain homeostasis assessment to estimate the uncertainty of the current model parameter when faced with novel-domain samples. Then, the Fisher information matrix is computed to measure the parameter sensitivity, with larger indicating the domain-sensitive parameter, and vice versa. Moreover, we propose an isolated parameter optimization strategy to update those domain-specific parameters to adapt to the new-domain, while preserving the invariant ones. In our experimental result, HoCoTTA outperforms the state-of-the-art approaches on several benchmarks, especially excelling in addressing continuous domain drifts, achieving a large improvement. More details and results could be found in the supplementary material.