The offshore wind industry is currently expanding into emerging markets at a rapid pace. Some of these markets are located in areas characterized by frequent extreme events. From a geotechnical perspective, this results in new design challenges, as foundations must withstand severe loads repeatedly throughout their intended lifetimes. Jacket structures resting on suction buckets represent a new foundation concept that still requires research to become a potential optimal solution. The vertical cyclic response of bucket foundations constitutes the main topic of this article. The current study is based on observations of the behavior of a scaled model installed in dense sand. Both normal and extreme conditions were simulated by applying axial cyclic loads of varying amplitudes, means, and frequencies. High amplitude and low frequency cause significant stiffness degradation and permanent displacement. These scenarios occur due to build-up of excess pore pressure, with subsequent triggering of liquefaction. A criterion for liquefaction occurrence is identified and may be readily used for practical applications. Considerable levels of tensile loading lead to a high rate of heave, regardless of frequency. For one-way compressive forces, after an extreme loading sequence, stiffness returns to its initial level, as long as no liquefaction develops priorly. This bears essential implications in predicting the change of natural frequency of the system.