Modern plankton high-throughput monitoring relies on deep learning classifiers for species recognition in water ecosystems. Despite satisfactory nominal performances, a significant challenge arises from Dataset Shift, which causes performances to drop during deployment. In our study, we integrate the ZooLake dataset with manually-annotated images from 10 independent days of deployment, serving as test cells to benchmark Out-Of-Dataset (OOD) performances. Our analysis reveals instances where classifiers, initially performing well in In-Dataset conditions, encounter notable failures in practical scenarios. For example, a MobileNet with a 92% nominal test accuracy shows a 77% OOD accuracy. We systematically investigate conditions leading to OOD performance drops and propose a preemptive assessment method to identify potential pitfalls when classifying new data, and pinpoint features in OOD images that adversely impact classification. We present a three-step pipeline: (i) identifying OOD degradation compared to nominal test performance, (ii) conducting a diagnostic analysis of degradation causes, and (iii) providing solutions. We find that ensembles of BEiT vision transformers, with targeted augmentations addressing OOD robustness, geometric ensembling, and rotation-based test-time augmentation, constitute the most robust model, which we call BEsT model. It achieves an 83% OOD accuracy, with errors concentrated on container classes. Moreover, it exhibits lower sensitivity to dataset shift, and reproduces well the plankton abundances. Our proposed pipeline is applicable to generic plankton classifiers, contingent on the availability of suitable test cells. By identifying critical shortcomings and offering practical procedures to fortify models against dataset shift, our study contributes to the development of more reliable plankton classification technologies.