Providing accurate prediction of the Burning Through Point (BTP) is crucial for enhancing both production quality and efficiency of sintering process. However, the sintering process is often influenced by various factors, including fluctuations in raw material quantities, equipment operational status, and environmental variations. These factors lead to distribution drift and introduce nonstationarity in process variables. Such complexities pose significant challenges for BTP prediction. To address these issues, this paper introduces  a novel Long Short-Term Memory model incorporating Reversible Instance Normalization and Time Convolution Networks (RTCN-LSTM) to mitigate the effects of distribution drift. The proposed model employs a position-symmetric reversible instance normalization (RevIN) module, which first normalizes input instances to eliminate nonstationary patterns, then precisely restores the original statistical properties at the output of model. The effectiveness of the proposed method is validated using the real-world sintering process data from a steel plant. Experimental results show that the proposed RTCN-LSTM model is significantly superior to other traditional methods in terms of performance and accuracy of multi-step BTP prediction, and it can effectively reduce the impact of distribution drift on the model prediction performance.