Several small polycyclic aromatic hydrocarbons (PAHs) with closed-shell electronic structure have been identified in the cold, dark environment Taurus Molecular Cloud 1. We measure efficient radiative cooling through the combination of recurrent fluorescence (RF) and IR emission in the closed-shell indenyl cation (C9H7+), finding good agreement with a master equation model including molecular dynamics trajectories to describe internal-energy-dependent properties for RF. We find that C9H7+ formed with up to Ec=5.85 eV vibrational energy, which is ≈2 eV above the dissociation threshold, radiatively cool rather than dissociate. The efficient radiative stabilization dynamics are likely common to other closed-shell PAHs present in space, contributing to their abundance.