Resistance to oseltamivir, the most widely used influenza antiviral drug, spread to fixation in seasonal influenza A(H1N1) between 2006 and 2009. This sudden rise in resistance seemed puzzling given the low overall level of the oseltamivir usage and the lack of a correlation between local rates of resistance and oseltamivir usage. We used a stochastic simulation model and deterministic approximations to examine how such events can occur, and in particular to determine how the rate of fixation of the resistant strain depends both on its fitness in untreated hosts as well as the frequency of antiviral treatment. We found that, for the levels of antiviral usage in the population, the resistant strain will eventually spread to fixation, if it is not attenuated in transmissibility relative to the drug-sensitive strain, but not at the speed observed in seasonal H1N1. The extreme speed with which the resistance spread in seasonal H1N1 suggests that the resistant strain had a transmission advantage in untreated hosts, and this could have arisen from genetic hitchhiking, or from the mutations responsible for resistance and compensation. Importantly, our model also shows that resistant virus will fail to spread if it is even slightly less transmissible than its sensitive counterpart--a finding of relevance given that resistant pandemic influenza (H1N1) 2009 may currently suffer from a small, but nonetheless experimentally perceptible reduction in transmissibility.