Super-resolution structured-illumination microscopy (SIM) is a powerful technique that allows one to surpass the diffraction limit by up to a factor two. Yet, its practical use is hampered by its sensitivity to imaging conditions which makes it prone to reconstruction artefacts. In this work, we present FlexSIM, a flexible SIM reconstruction method capable to handle highly challenging data. Specifically, we demonstrate the ability of FlexSIM to deal with the distortion of patterns, the high level of noise encountered in live imaging, as well as out-of-focus fluorescence. Moreover, we show that FlexSIM achieves state-of-the-art performance over a variety of open SIM datasets.