We develop a framework that casts the point water-vegetation dynamics under stochastic rainfall forcing as a continuous-time random walk (CTRW), which yields an evolution equation for the joint probability density function (PDF) of soil-moisture and biomass. We find regime shifts in the steady-state PDF as a consequence of changes in the rainfall structure, which flips the relative strengths of the system attractors, even for the same mean precipitation. Through an effective potential, we quantify the impact of rainfall variability on ecosystem resilience and conclude that amplified rainfall regimes reduce the resilience of water-stressed ecosystems, even if the mean annual precipitation remains constant.Spain. Ministerio de Economia y Competitividad ("Ramon y Cajal" Fellowship Grant RyC-2012-11704)