A key challenge in processing electrocardiogram (ECG) signals for personalized biometric authentication systems is the efficient retraining of deep learning models when new user data become available. This study employs a transfer learning approach combined with the VGG16 architecture to investigate the permissible threshold for repeatedly integrating data from a single user—assigned with varying access labels—into a pre-trained base model. The base model was initially trained on 46 users from the MIT-BIH database. For each target user, data were simulated across 100 iterations with random label assignments and incrementally incorporated via gradual fine-tuning. The results reveal that the final model's performance improves with the addition of up to approximately 44 to 46 target models—a quantity comparable to the number of initial users—after which performance declines. The optimal range for adding new data from a single user was identified as 11 to 16 iterations. Within this interval, the model achieves an accuracy exceeding 99% without exhibiting catastrophic forgetting. These findings confirm that while transfer learning offers an efficient mechanism for frequent updates in ECG-based biometric systems, it possesses a finite capacity for accommodating repeated modifications. Determining this threshold provides valuable practical guidance for the development of security and health monitoring systems that must balance functional flexibility with overall model stability.