One weakness of machine-learning algorithms is the need to train the models for a new task. This presents a specific challenge for biometric recognition due to the dynamic nature of databases and, in some instances, the reliance on subject collaboration for data collection. In this paper, we investigate the behavior of deep representations in widely used CNN models under extreme data scarcity for One-Shot periocular recognition, a biometric recognition task. We analyze the outputs of CNN layers as identity-representing feature vectors. We examine the impact of Domain Adaptation on the network layers' output for unseen data and evaluate the method's robustness concerning data normalization and generalization of the best-performing layer. We improved state-of-the-art results that made use of networks trained with biometric datasets with millions of images and fine-tuned for the target periocular dataset by utilizing out-of-the-box CNNs trained for the ImageNet Recognition Challenge and standard computer vision algorithms. For example, for the Cross-Eyed dataset, we could reduce the EER by 67% and 79% (from 1.70% and 3.41% to 0.56% and 0.71%) in the Close-World and Open-World protocols, respectively, for the periocular case. We also demonstrate that traditional algorithms like SIFT can outperform CNNs in situations with limited data or scenarios where the network has not been trained with the test classes like the Open-World mode. SIFT alone was able to reduce the EER by 64% and 71.6% (from 1.7% and 3.41% to 0.6% and 0.97%) for Cross-Eyed in the Close-World and Open-World protocols, respectively, and a reduction of 4.6% (from 3.94% to 3.76%) in the PolyU database for the Open-World and single biometric case.