Although we develop influenza immunity from an early age, it is insufficient to prevent future infection with antigenically novel strains. One proposed way to generate long-term protective immunity against a broad range of influenza virus strains is to boost responses to the conserved epitopes on the hemagglutinin, the major surface glycoprotein on the influenza virus. Influenza-specific humoral immunity comprises a large fraction of the overall immune memory in humans, and it has been long recognized that preexisting immunity to influenza shapes the response to subsequent influenza infections and vaccinations. However, the mechanisms by which preexisting immunity modulates the response to influenza vaccination are still not completely understood. Using a set of mathematical models, we explore several hypotheses that may contribute to diminished boosting of antibodies to conserved epitopes after repeated vaccinations.