This paper proposes a robust method to screen patients with sleep apnea syndrome (SAS) using a single-lead electrocardiogram (ECG). This method consists of minute-by-minute abnormal breathing detection and apnea-hypopnea index (AHI) estimation. Heartbeat interval and ECG-derived respiration (EDR) are calculated using the single-lead ECG and used to train the models, including ResNet18, ResNet34, and ResNet50. The proposed method, using data from 1232 subjects, was developed with two open datasets and experimental data and evaluated using two additional open datasets and data acquired from an abdomen-attached wearable device (in total, data from 189 subjects). ResNet18 showed the best results, having an average Cohen's kappa coefficient of 0.57, in the abnormal breathing detection. Moreover, SAS patient classification, with 15 as the AHI threshold, yielded an average Cohen's kappa coefficient of 0.71. The results of patient classification were biased toward data from the wearable patch-type device, which may be influenced by different ECG waveforms. The proposed method is tuned with a sample of the data from the device, and the performance result of Cohen's kappa increased from 0.54 to 0.91 for SAS patient classification. Our method, proposed in this paper, achieved equivalent performance results with data recorded using an abdomen-attached wearable device and two open datasets used in previous studies, although the method had not used those data during model training. The proposed method could reduce the development costs of commercial software, as it was developed using open datasets, has robust performance throughout all datasets.