An increase in biological diversity leads to a greater stability of ecosystem properties. For host-parasite interactions, this is illustrated by the 'dilution effect': a negative correlation between host biodiversity and disease risk. We show that a similar mechanism might stabilise host-parasite dynamics at a lower level of diversity, i.e. at the level of genetic diversity within host species. A long-term time shift experiment, based on a historical reconstruction of a Daphnia-parasite coevolution, reveals infectivity cycles with more stable amplitude in experienced than in naive hosts. Coevolutionary models incorporating an increase in host allelic diversity over time explain the detected asymmetry. The accumulation of resistance alleles creates an opportunity for the host to stabilise Red Queen dynamics. It leads to a larger arsenal enhancing the host performance in its coevolution with the parasite in which 'it takes all the running both antagonists can do to keep in the same place'.