Two-thirds of all glaciers worldwide are projected to disappear by 2100 CE. Large uncertainties however remain in maritime settings, where some glaciers have recently gained mass in response to increased snowfall. One of these regions is southern Patagonia, where increased precipitation since the 1980s seems to have attenuated glacier retreat. Whether this exceptional behavior will continue in a warmer future is unclear. Here, we use a numerical ice-flow model constrained by paleoglaciological data to simulate how climate variability influenced the evolution of three maritime outlet glaciers of the Southern Patagonian Icefield during the last 6000 years. Our experiments suggest that precipitation drove 67% of the centennial-scale fluctuations in the volume of the modeled glaciers. When applied to the temperature projected by 2100 CE, our simulations show that precipitation needs to increase by 10-50% to maintain present-day glacier volumes, depending on the climate scenario (SSP1-2.6 to SSP5-8.5). This implies that if greenhouse-gas emission cuts fail, these glaciers will enter a warmer regime unseen over the last 6000 years, where precipitation cannot offset glacier mass loss. Conversely, if emissions are curtailed, increased precipitation could halt mass loss of some of Patagonia's largest glaciers, and potentially of other maritime glaciers worldwide.