Fluorogen-binding tags, which activate the fluorescence of a specific chromophore (so-called fluorogen) upon reversible binding, have recently been proposed as a way of reducing photobleaching via fluorogen renewal. However, no generic methodology has been proposed to systematically analyze the photodamage of the fluorogen and the protein tag. Using Y-FAST (Yellow Fluorescence-activating and Absorption-Shifting Tag) as a case study we propose here a generic experimental and theoretical approach to assess how fluorogen renewal reduces the apparent photobleaching rate of a fluorogen-binding tag. Y-FAST has its apparent photobleaching rate greatly reduced by fluorogen renewal and its photostability is mainly limited by oxidation of specific residues in the protein scaffold by reactive oxygen species generated by the bound fluorogen. This study sets the groundwork for the optimization of fluorogenic systems, helping guide rational improvements to their photostability.