This paper proposes a few-shot method based on Faster R-CNN and representation learning for object detection in aerial images. The two classification branches of Faster R-CNN are replaced by prototypical networks for online adaptation to new classes. These networks produce embeddings vectors for each generated box, which are then compared with class prototypes. The distance between an embedding and a prototype determines the corresponding classification score. The networks are trained in an episodic manner. A new detection task is randomly sampled at each epoch, consisting in detecting only a subset of the classes annotated in the dataset. This strategy encourages the network to adapt to new classes as it would at test time. In addition, several ideas are explored to improve the proposed method such as a hard negative examples mining strategy and self-supervised clustering for background objects. The performance of our method is assessed on DOTA, a large-scale remote sensing images dataset. The experiments conducted provide a broader understanding of the capabilities of representation learning. It highlights in particular some intrinsic weaknesses for the few-shot object detection task. Finally, some suggestions and perspectives are formulated according to these insights.