Large-eddy simulation (LES) is often used as a benchmark simulation in climate science and is suggested as a fundamental tool to examine, e.g., marine cloud brightening. Therefore, it is necessary to critically evaluate if these high-resolution models can skillfully simulate expected physical phenomena. This study focuses on the first indirect aerosol effect in warm stratocumulus clouds. We investigate if an LES code with explicit aerosol-cloud interactions and a widely used two-moment bulk microphysical scheme can reproduce well-known cloud droplet number susceptibility regimes previously identified by observations and supported by detailed parcel model simulations—the updraft-limited regime (typically occurring at high aerosol number concentrations and low updraft speeds) and the aerosol-limited regime (typically occurring at low aerosol number concentrations and high updraft speeds). Our simulations show that the LES in its default configuration cannot reproduce the two regimes if the initial droplet radius of newly activated droplets (rid) is estimated by integrating the wet aerosol size distribution. The main reason is related to the relatively coarse (but commonly used) time step in the model (Δt ≈ 1s), which is too long to resolve relevant microphysical processes adequately at high aerosol concentrations. A regime transition does occur if the timestep is decreased to Δt ≈ 0.1s and if a renormalization procedure is applied, which limits the number of activated droplets so that the water mass of the newly activated droplets cannot exceed the available amount of supersaturated water vapor. Another way to obtain a regime transition is to increase rid to values >1 µm. However, a clear recommendation for the choice of rid cannot be made upon physical arguments. An alternative solution could be to introduce a sub-time-stepping or adaptive time-stepping algorithm to calculate droplet formation and growth, particularly for updraft-limited conditions. Our study highlights the importance of critically evaluating LES results to guarantee that relevant physical processes are properly represented.