Bronchiolitis Obliterans Syndrome (BOS), a fibrotic airway disease following lung transplantation, conventionally relies on pulmonary function tests (PFTs) for diagnosis due to limitations of CT images. Thus far, deep neural networks (DNNs) have not been used for BOS detection. We optimized a DNN for detection of BOS solely using CT scans by integrating an innovative co-training method for enhanced performance in low-data scenarios. The novel auxiliary task is to predict the temporal precedence of CT scans of BOS patients. We tested our method using CT scans at various stages of inspiration from 75 post-transplant patients, including 26 with BOS. The method achieved a ROC-AUC of 0.90 (95% CI: 0.840-0.953) in distinguishing BOS from non-BOS CT scans. Performance correlated with disease progression, reaching 0.88 ROC-AUC for stage I, 0.91 for stage II, and an outstanding 0.94 for stage III BOS. Importantly, performance parity existed between standard and high-resolution scans. Particularly noteworthy is the DNN's ability to predict BOS in at-risk patients (FEV1 between 80% and 90% of best FEV1) with a robust 0.87 ROC-AUC (CI: 0.735-0.974). Using techniques for visually interpreting the results of deep neural networks, we reveal that our method is especially sensitive to hyperlucent areas compatible with air-trapping or bronchiectasis. Our approach shows the potential to improve BOS diagnosis, enabling early detection and management. Detecting BOS from low-resolution scans reduces radiation exposure and using scans at any stage of respiration makes our method more accessible. Additionally, we demonstrate that techniques that limit overfitting are essential to unlocking the power of DNNs in scenarios with scarce training data. Our method may enable clinicians to use DNNs in studies where only a modest number of patients is available.