Extensive valley glaciers have repeatedly covered the inner gorges of the Swiss Alps during Quaternary glaciations. Two controversial explanations of the development of the features have been proposed. In the first, the gorges would have formed anew each time the glaciers receded, through fluvial incision of the previously glaciated surfaces. Alternatively, the valleys could be palimpsest features, carved through successive glacial-interglacial cycles. Here we use topographic data derived from LiDAR measurements to show that fluvial erosion rates of 8.5-18 mm yr^-1 would be required to create the current relief of Swiss gorges solely during the present interglacial period. Such high rates exceed the long-term average bedrock erosion rates of even the most tectonically active regions. This scenario would also require that previously incised valleys were erased during successive glaciations by commensurately high glacial erosion rates, a suggestion that is incompatible with available constraints of exhumation from thermochronometry. We therefore suggest that the gorges observed in the Swiss Alps are resilient to repeated glaciations. Our data are most consistent with the hypothesis that gorges are progressively incised below the elevations of glacial trough valleys through multiple glaciations.