Sensor failures, communication interruptions, and other monitoring problems can lead to missing acceleration responses in structural health monitoring of offshore platforms. To address this issue, a hierarchical feature fusion reconstruction (HFFR) method is proposed. The method employs multi-scale local morphology encoding to characterize local response morphology over different temporal neighborhoods, uses bidirectional temporal modeling to capture response evolution before and after the missing data, and adaptively weights temporal information according to feature correlation. A dataset is constructed using numerical simulation data from an offshore platform under different wave–current conditions, and the proposed method is evaluated through ablation and comparative experiments. After introducing multi-scale local morphology encoding and adaptive feature weighting into the bidirectional temporal modeling framework, the RMSE decreases from 0.5036 to 0.1109, while R² increases from 0.7581 to 0.9883, confirming the effectiveness of the hierarchical information representation framework. The results show that HFFR can recover the major peaks and valleys, amplitude envelopes, and local fluctuations of the missing responses, thereby improving both reconstruction accuracy and the preservation of dynamic response characteristics. The current validation is mainly based on high-fidelity numerical simulations; therefore, the applicability of the proposed method in real monitoring environments should be further verified through physical model tests.