Large rhyolitic volcanoes pose a hazard, yet the processes and signals foretelling an eruption are obscure. Satellite geodesy has revealed surface inflation signaling unrest within magma reservoirs underlying a few rhyolitic volcanoes. Although seismic, electrical, and potential field methods may illuminate the current configuration and state of these reservoirs, they cannot fully address the processes by which they grow and evolve on geologic time scales. We combine measurement of a deformed paleoshore surface, isotopic dating of volcanism and surface exposure, and modeling to determine the rate of growth of a rhyolite-producing magma reservoir. The numerical approach builds on a magma intrusion model developed to explain the current, decade-long, surface inflation at >20 cm/year. Assuming that the observed 62-m uplift reflects several non-eruptive intrusions of magma, each similar to the unrest over the past decade, we find that ~13 km3 of magma recharged the reservoir at a depth of ~7 km during the Holocene, accompanied by the eruption of ~9 km3 of rhyolite. The long-term rate of magma input is consistent with reservoir freezing and pluton formation. Yet, the unique set of observations considered here implies that large reservoirs can be incubated and grow at shallow depth via episodic high-flux magma injections. These replenishment episodes likely drive rapid inflation, destabilize cooling systems, propel rhyolitic eruptions, and thus should be carefully monitored.