Host-virus association data underpin research into the distribution and eco-evolutionary correlates of viral diversity and zoonotic risk across host species. However, current knowledge of the wildlife virome is inherently constrained by historical discovery effort, and there are concerns that the reliability of ecological inference from host-virus data may be undermined by taxonomic and geographical sampling biases. Here, we evaluate whether current estimates of host-level viral diversity in wild mammals are stable enough to be considered biologically meaningful, by analysing a comprehensive dataset of discovery dates of 6571 unique mammal host-virus associations between 1930 and 2018. We show that virus discovery rates in mammal hosts are either constant or accelerating, with little evidence of declines towards viral richness asymptotes, even in highly sampled hosts. Consequently, inference of relative viral richness across host species has been unstable over time, particularly in bats, where intensified surveillance since the early 2000s caused a rapid rearrangement of species' ranked viral richness. Our results illustrate that comparative inference of host-level virus diversity across mammals is highly sensitive to even short-term changes in sampling effort. We advise caution to avoid overinterpreting patterns in current data, since it is feasible that an analysis conducted today could draw quite different conclusions than one conducted only a decade ago.