Existing prediction models that rely on static architectures and fixed receptive fields often have difficulty handling complex non-stationary behaviors such as sudden state transitions, transient anomalies, and heterogeneous frequency patterns that are common in real-world time series. These characteristics pose a major challenge to models that lack spectral filtering and adaptive reasoning capabilities, severely limiting their effectiveness in capturing changing temporal dynamics. To address this critical challenge, we propose a Temporal-Spiking-Spatial-Attention Network (TSSA-Net), which integrates two complementary modules: a frequency-based spatial-temporal attention (FSTA) and a just-in-time dynamic adaptor (JITDA). Inspired by Spiking Neural Networks, FSTA employs frequency-aware filtering and attention mechanisms to actively suppress noise and enhance salient signal patterns. JITDA leverages Just-in-Time Learning principles to dynamically calibrate predictions during inference, endowing the model with rapid adaptability to concept drift. Extensive experiments on multiple large-scale benchmark datasets demonstrate that TSSA-Net significantly outperforms all baseline methods, including the latest state-of-the-art models, showcasing its superior robustness and effectiveness in complex non-stationary environments.