Radar-based human activity recognition (HAR) is a popular research field. Despite claims of high accuracy on self-collected datasets, the ability of these models to handle unexpected scenarios has been largely overlooked. This work introduces a framework for analyzing corruption robustness of radar micro-Doppler spectrogram classification. A set of corruptions are categorized, applied, and systematically tested on common model architectures. Diverse training methods, including adversarial training, cadence velocity diagram (CVD) transformation and data augmentation, are explored. The performance is evaluated on two tasks: indoor HAR and continuous aquatic HAR. Our study unveils several insights. Firstly, relying solely on accuracy may not adequately assess model performance due to dataset limitations. All well-trained models exhibit sensitivity to corruptions. Secondly, deeper convolutional neural network (CNN) models excel in both accuracy and robustness, but confront the problem of overfitting to background. Thirdly, adversarial training enhances robustness against corruptions, albeit at the cost of a slight decrease in accuracy. Lastly, combining data augmentation and adversarial training achieves a balance between accuracy and robustness. In essence, our study contributes to a more profound understanding of the complex interplay between model architecture, classification accuracy, and corruption robustness in radar HAR tasks.