The monophagous flightless weevil Hadramphus spinipennis causes the frequent local extinction of its host plant Aciphylla dieffenbachii through overexploitation. Both species are endemic and restricted to the Chatham Islands group (New Zealand). The weevil is classified as endangered and the plant as a threatened species. As this herbivore-plant system is locally unstable long-term persistence only appears possible via a metapopulation structure in which subpopulations are connected by dispersal. This paper investigates this hypothesis using a spatially explicit model of a consumer population whose resource is patchily distributed. The parameters are adapted to the H. spinipennis-A. diffenbachii system. Our model includes local population dynamics and dispersal of the consumer, the destruction of host plant patches due to foraging and their regeneration. The results show that the key factor for long-term persistence is the short-range dispersal of the consumer with high mortality during dispersal. Only this highly inefficient dispersal prevents the synchronisation of local dynamics while ensuring sufficient colonisation of regenerated patches. We also show that although synchronisation through spatially correlated environmental fluctuations may be critical for long-term persistence, it cannot replace the strong effects of dispersal. Thus, in a consumer-resource metapopulation with deterministic local extinction, the strength and spatial scale of consumer dispersal in relation to the spatial and temporal scales of the resource patch dynamics (patch destruction and regeneration, number. size and distance of patches) play a vital role for long-term persistence. The consequence for conservation management is that such metapopulations could in fact profit rather than suffer from decreasing connectivity of resource patches.