In chronic viral infection, low levels of viral replication and infectious particle production are maintained over long periods, punctuated by brief bursts of high viral production and release. We apply well-established principles of modelling virus dynamics to the study of chronic viral infection, demonstrating that a model which incorporates the distinct contributions of cytotoxic T lymphocytes (CTLs) and antibodies exhibits long periods of quiescence followed by brief bursts of viral production. This suggests that for recurrent viral infections, no special mechanism or exogenous trigger is necessary to provoke an episode of reactivation; rather, the system may naturally cycle through recurrent episodes at intervals which can be many years long. We also find that exogenous factors which cause small fluctuations in the natural course of the infection can trigger a recurrent episode. Our model predicts that longer periods between recurrences are associated with more severe viral episodes. Four factors move the system towards less frequent, more severe episodes: decreased viral infectivity, decreased CTL efficacy, decreased memory T cell response and increased antibody efficacy.