This study investigates the effect of structural damping on vortex-induced vibration (VIV)of a circular cylinder when the mass ratio is below its critical value. It is confirmedby water-channel experiments and a reduced-order model (ROM) that the previouslyidentified phenomenon of VIV forever, i.e. resonance oscillations at any reduced velocity,persists even with high structural damping. Of interest, the ROM results reveal that thewake mode for VIV forever is unstable with a constant positive growth rate with increasingreduced velocity, while the experimental results suggest that VIV forever is associatedwith a synchronisation between the non-stationary cylinder vibration frequency and thevortex-shedding frequency