Mirror modes are ubiquitous in space plasma and grow from pressure anisotropy. Together with other instabilities, they play a fundamental role in constraining the free energy contained in the plasma. This study focuses on mirror modes observed in the solar wind by Solar Orbiter for heliocentric distances between 0.5 and 1 AU. Typically, mirror modes have timescales from several to tens of seconds and are considered quasi-MHD structures. In the solar wind, they also generally appear as isolated structures. However, in certain conditions, prolonged and bursty trains of higher frequency mirror modes are measured, which have been labeled previously as mirror mode storms. At present, only a handful of existing studies have focused on mirror mode storms, meaning that many open questions remain. In this study, Solar Orbiter has been used to investigate several key aspects of mirror mode storms: their dependence on heliocentric distance, association with local plasma properties, temporal/spatial scale, amplitude, and connections with larger-scale solar wind transients. The main results are that mirror mode storms often approach local ion scales and can no longer be treated as quasi-MHD, thus breaking the commonly used long-wavelength assumption. They are typically observed close to current sheets and downstream of interplanetary shocks. The events were observed during slow solar wind speeds and there was a tendency for higher occurrence closer to the Sun. The occurrence is low, so they do not play a fundamental role in regulating ambient solar wind but may play a larger role inside transients.