Fault diagnosis for embedded sensors in asphalt pavement faces significant challenges, including the scarcity of real-world fault data and the difficulty in identifying compound faults, which severely compromises the reliability of monitoring data. To address these issues, this study proposes an intelligent diagnostic framework that integrates a Discrete Wavelet Transform (DWT) with a staged, attention-based Long Short-Term Memory (LSTM) network. First, various fault modes were systematically defined, including short-term (i.e., bias, gain, and detachment), long-term (i.e., drift), and their compound forms. A fine-grained fault injection and labeling strategy was then developed to generate a comprehensive dataset. Second, a novel diagnostic model was designed based on a “Decomposition-Focus-Fusion” architecture. In this architecture, the DWT is employed to extract multi-scale features, and independent sub-models—a Bidirectional LSTM (Bi-LSTM) and a stacked LSTM—are subsequently utilized to specialize in learning short-term and long-term fault characteristics, respectively. Finally, an attention network intelligently weights and fuses the outputs from these sub-models to achieve precise classification of eight distinct sensor operational states. Validated through rigorous 5-fold cross-validation, experimental results demonstrate that the proposed framework achieves a mean diagnostic accuracy of 98.89% (±0.0040) on the comprehensive test set, significantly outperforming baseline models such as SVM, KNN, and a unified LSTM. A comprehensive ablation study confirmed that each component of the “Decomposition-Focus-Fusion” architecture—DWT features, staged training, and the attention mechanism—makes an indispensable contribution to the model’s superior performance. The model successfully distinguishes between “drift” and “normal” states—which severely confuse the baseline models—and accurately identifies various complex compound faults. Furthermore, simulated online diagnostic tests confirmed the framework’s rapid response capability to dynamic faults and its computational efficiency, meeting the demands of real-time monitoring. This study offers a precise and robust solution for the fault diagnosis of embedded sensors in asphalt pavement.