Pre-trained models have demonstrated exceptional generalization capabilities in time-series forecasting; however, adapting them to evolving data distributions remains a significant challenge. A key hurdle lies in accessing the original training data, as fine-tuning solely on new data often leads to catastrophic forgetting. To address this issue, we propose Replay Tuning (R-Tuning), a novel framework designed for the continual adaptation of pre-trained time-series models. R-Tuning constructs a unified latent space that captures both prior and current task knowledge through a frequency-aware replay strategy. Specifically, it augments model-generated samples via wavelet-based decomposition across multiple frequency bands, generating trend-preserving and fusion-enhanced variants to improve representation diversity and replay efficiency. To further reduce reliance on synthetic samples, R-Tuning introduces a latent consistency constraint that aligns new representations with the prior task space. This constraint guides joint optimization within a compact and semantically coherent latent space, ensuring robust knowledge retention and adaptation. Extensive experimental results demonstrate the superiority of R-Tuning, which reduces MAE and MSE by up to 46.9% and 46.8%, respectively, on new tasks, while preserving prior knowledge with gains of up to 5.7% and 6.0% on old tasks. Notably, under few-shot settings, R-Tuning outperforms all state-of-the-art baselines even when synthetic proxy samples account for only 5% of the new task dataset. Implementation details and code are provided in the supplementary material.