Fatigue in air traffic controllers (ATCOs), particularly within remote tower operations, poses a substantial risk to aviation safety due to its detrimental effects on vigilance, decision-making, and situational awareness. While electroencephalography (EEG) provides a promising avenue for objective fatigue monitoring, existing models often fail to adequately capture both the spatial dependencies across brain regions and the temporal dynamics of cognitive states. To address this challenge, we propose a novel EEG-based fatigue detection framework, Spatio-Temporal Graph with Center Loss Network (STG-CLNet), which jointly models topological brain connectivity and temporal EEG evolution. The model leverages a multi-stage graph convolutional network to encode spatial dependencies and a triple-layer LSTM module to capture temporal progression, while incorporating center loss to enhance feature discriminability in the embedding space. We constructed a domain-specific EEG dataset involving 34 ATCO participants operating in high- and low-traffic remote tower simulations, with fatigue labels derived from three validated subjective metrics. Experimental results demonstrate that STG-CLNet achieves superior classification performance (accuracy = 96.73%, recall = 92.01%, F1-score = 87.15%), outperforming several strong baselines, including LSTM and EEGNet. These findings underscore the potential of STG-CLNet for integration into real-time cognitive monitoring systems in air traffic control, contributing to both theoretical advancement and operational safety enhancement.