Intracellular structure such as endoplasmic reticulum and mitochondrion is a significant topic in life science. In which, intracellular structures segmentation based on fluorescence microscopy (FM) images plays an important role in morphological analysis and clinical application of biological cells. However, due to natural interferences, FM image acquisition is usually unstable, resulting in degraded images. When deep neural network (DNN) models segment intracellular structures on these corrupted images, they often behave low robustness, namely, their extracted structures are unsatisfactory. To obtain more stable DNN models for widespread deployment in practice, we need to solve this problem. Therefore, this paper is committed to improving the corruption robustness of DNN models, so that they possess a stronger ability to deal with corrupted FM images. First, we propose three data augmentations to diversify the training data distributions. Second, we design experiments and find that flatter loss landscape is generally associated with higher corruption robustness. Therefore, LayerSAM-DA-Seg is proposed, a method that combines layer adaptive sharpness-aware minimization (LayerSAM) and data augmentation (DA) together. This method helps DNN models converge to flatter minima, thus gaining stronger robustness. At the same time, data augmentation will push models to memorize diverse data distributions, thus gaining greater ability to process corrupted data. Experiments indict that compared with single optimization, the combination of LayerSAM and data augmentation will achieve greater gains. Our LayerSAM-DA-Seg achieves the most stable intracellular structures segmentation on corrupted FM images. The code is available at https://github.com/cbmi-group/Improve-Robustness-of-ICS .