Pigs have long been hypothesized to play a central role in the emergence of novel human influenza A virus (IAV) strains, by serving as mixing vessels for mammalian and avian variants. However, the key issue of viral persistence in swine populations at different scales is ill understood. We address this gap using epidemiological models calibrated against seroprevalence data from Dutch finishing pigs to estimate the 'critical herd size' (CHS) for IAV persistence. We then examine the viral phylogenetic evidence for persistence by comparing human and swine IAV. Models suggest a CHS of approximately 3000 pigs above which influenza was likely to persist, i.e. orders of magnitude lower than persistence thresholds for IAV and other acute viruses in humans. At national and regional scales, we found much stronger empirical signatures of prolonged persistence of IAV in swine compared with human populations. These striking levels of persistence in small populations are driven by the high recruitment rate of susceptible piglets, and have significant implications for management of swine and for overall patterns of genetic diversity of IAV.