This paper presents a comprehensive study on fall recognition and forecasting for reconfigurable stair-accessing robots by leveraging deep learning techniques. The proposed framework integrates machine learning algorithms and recurrent neural networks (RNNs), specifically Long Short-Term Memory (LSTM) and Bidirectional LSTM (BiLSTM), for fall detection of service robots on staircases. The reconfigurable stair-accessing robot sTetro serves as the platform, and the fall data required for training models are generated in a simulation environment. The two machine learning algorithms are compared and their effectiveness on the fall recognition task is reported. The results indicate that the BiLSTM model effectively classifies falls with a median categorical accuracy of 94.10% in simulation and 90.02% with limited experiments. Additionally, the BiLSTM model can be used for forecasting, which is practically valuable for making decisions well before the onset of a free fall. This study contributes insights into the design and implementation of fall detection systems for service robots used to navigate staircases through deep learning approaches. Our experimental and simulation data, along with the simulation steps, are available for reference and analysis via the shared link.