Pathogen circulation among reservoir hosts is a precondition for zoonotic spillover. Unlike the acute, high morbidity infections typical in spillover hosts, infected reservoir hosts often exhibit low morbidity and mortality. Although it has been proposed that reservoir host infections may be persistent with recurrent episodes of shedding, direct evidence is often lacking. We construct a generalised SEIR (susceptible, exposed, infectious, recovered) framework encompassing 46 sub-models representing the full range of possible transitions among those four states of infection and immunity. We then use likelihood-based methods to fit these models to nine years of longitudinal data on henipavirus serology from a captive colony of Eidolon helvum bats in Ghana. We find that reinfection is necessary to explain observed dynamics; that acute infectious periods may be very short (hours to days); that immunity, if present, lasts about 1-2 years; and that recurring latent infection is likely. Although quantitative inference is sensitive to assumptions about serology, qualitative predictions are robust. Our novel approach helps clarify mechanisms of viral persistence and circulation in wild bats, including estimated ranges for key parameters such as the basic reproduction number and the duration of the infectious period. Our results inform how future field-based and experimental work could differentiate the processes of viral recurrence and reinfection in reservoir hosts.