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We present a hypothesis that best explains cosmogenic isotope data on blue-ice moraines in the Heritage Range, West Antarctica. The age of the moraines implies that they, and the related ice-sheet surface with which they are associated, have persisted on the flanks of nunataks throughout at least the last interglacial/glacial cycle. The implication is that although the West Antarctic Ice Sheet (WAIS) may have fluctuated in thickness during glacial cycles, the central dome has remained intact for at least 200kyr and possibly even for 400kyr. Such a finding, if substantiated, would contribute to our understanding of the sensitivity of the WAIS to climate change. Further it would be a powerful geomorphic constraint on models of the past behaviour of the ice sheet during glacial cycles and thus those predicting the future of the ice sheet in a warming world.