Epithermal ore deposits are important resources for various precious (e.g. Au, Ag) and base (e.g. Cu, Pb, Zn) metals. They form within the uppermost 1.5 km of Earth's crust by circulation of hydrothermal fluids through fractured and porous rocks in geothermal and volcanic systems. Many hydrothermal veins in epithermal deposits show evidence for pulsed ore formation events with high metal contents limited to distinct growth zones. As a particularly efficient mechanism for metal enrichment to economic grades, transport and precipitation of precious metals has been proposed to occur by isochemical contraction of a magmatic vapor phase from an underlying magmatic-hydrothermal system, where fluids can phase separate, followed by a second phase-separation event of near-surface boiling. Numerical models can provide unique insights into the temporal and spatial relationships of ore-forming processes. We use a model for magma reservoir growth to investigate the impact of sill injection rates on the hydrothermal system. The simulations with more episodic, low injection rates (<1.3 x10-3 km³/y) result in a highly variable fluid plume which allows almost pure magmatic fluids to migrate to shallower and cooler regions, where they can phase separate and potentially form epithermal ore deposits. The modelling results point towards a relatively short time span of potential ore formation of a few thousands of years until the magmatic fluid plume retreats. Long-lived magma reservoirs which are forming at higher injection rates hamper the formation of high-grade epithermal deposits, but are more favourable for high-grade porphyry Cu deposits.