Missing acceleration responses caused by sensor faults and transmission interruptions can compromise the reliability of structural health monitoring for offshore platforms. To address continuous data loss, this study proposes a hierarchical feature fusion reconstruction (HFFR) method. HFFR organizes response information at three complementary levels. Multi-scale local response morphology encoding captures local dynamic characteristics over different temporal neighborhoods, bidirectional temporal modeling exploits response evolution before and after the missing segment, and correlation-based adaptive feature weighting emphasizes temporal information that is more relevant to reconstruction. The method is validated using numerical acceleration responses from a jacket offshore platform under multiple wave-current conditions and long-term measured responses from the Hardanger Bridge. Ablation studies confirm the complementary contributions of the three information levels, while comparisons with CNN-LSTM and BiLSTM-SA demonstrate improved reconstruction accuracy and better preservation of response characteristics. Time-domain and frequency-domain analyses further show that HFFR can recover major waveform variations and principal dynamic frequency components. Additional measured-data experiments under different continuous missing ratios demonstrate stable performance as data loss increases. These results demonstrate the effectiveness of HFFR for continuous missing-response reconstruction across the evaluated numerical and measured datasets, while more complex missing patterns and noise conditions remain to be investigated.