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Apnoea of prematurity is characterised by recurrent episodes of cessation of breathing and remains difficult to detect reliably using routinely monitored physiological signals in the Neonatal Intensive Care Unit (NICU). Existing bedside monitors rely primarily on respiratory rate and oxygen saturation thresholds, often generating high false-positive alarm rates and missing short or irregular events. Improving automated detection using routinely acquired clinical signals could enhance identification of clinically meaningful events without additional sensing hardware. We evaluated deep learning-based detection of apnoea-related Cessation Of BrEathing (COBE) events using impedance pneumography (IP), electrocardiography (ECG), and photoplethysmography (PPG) signals from approximately 430 hours of NICU recordings collected from 24 pre-term infants. Three independent reviewers annotated COBE events, producing a dataset of 346 COBE and 608 non-COBE events. We compared a shallow convolutional neural network (CNN), residual networks (ResNets), and a ConvNeXt architecture using an independent held-out test set. Across all architectures, detection performance was influenced more strongly by signal modality than by architectural complexity. Unimodal IP-based models achieved balanced accuracies of 86.8-88.0%, outperforming ECG-derived (62.6-69.7%) and PPG-derived (65.1-66.4%) respiratory surrogates. Multimodal fusion yielded modest improvements over IP alone. The best-performing model, a ConvNeXt architecture combining IP and PPG inputs, achieved 88.7% balanced accuracy and an F1 score of 0.75 on the independent test set. These findings demonstrate that deep learning models applied to routinely monitored NICU signals can reliably detect COBE events and highlight the importance of signal modality in data-constrained neonatal monitoring settings.