Accurate Remaining Useful Life (RUL) prediction is a key requirement for effective Prognostics and Health Management (PHM) in safety-critical systems such as aero-engines. Existing deep learning approaches, particularly LSTM-based models, often struggle to generalize across varying operating conditions and are sensitive to noise in multivariate sensor data. To address these challenges, we propose a novel Bidirectional Residual Corrected LSTM (Bi-cLSTM) model for robust RUL estimation. The proposed architecture combines bidirectional temporal modeling with an adaptive residual correction mechanism to iteratively refine sequence representations. In addition, we introduce a condition-aware preprocessing pipeline incorporating regime-based normalization, feature selection, and exponential smoothing to improve robustness under complex operating environments. Extensive experiments on all four subsets of the NASA C-MAPSS dataset demonstrate that the proposed Bi-cLSTM consistently outperforms LSTM-based baselines and achieves competitive state-of-the-art performance, particularly in challenging multi-condition scenarios. These results highlight the effectiveness of combining bidirectional temporal learning with residual correction for reliable RUL prediction.