ABSTRACT The presence of CO gas around 10–50 Myr old A stars with debris discs has sparked debate on whether the gas is primordial or secondary. Since secondary gas released from planetesimals is poor in H2, it was thought that CO would quickly photodissociate never reaching the high levels observed around the majority of A stars with bright debris discs. Kral et al. showed that neutral carbon produced by CO photodissociation can effectively shield CO and potentially explain the high CO masses around 9 A stars with bright debris discs. Here, we present a new model that simulates the gas viscous evolution, accounting for carbon shielding and how the gas release rate decreases with time as the planetesimal disc loses mass. We find that the present gas mass in a system is highly dependant on its evolutionary path. Since gas is lost on long time-scales, it can retain a memory of the initial disc mass. Moreover, we find that gas levels can be out of equilibrium and quickly evolving from a shielded on to an unshielded state. With this model, we build the first population synthesis of gas around A stars, which we use to constrain the disc viscosity. We find a good match with a high viscosity (α ∼ 0.1), indicating that gas is lost on time-scales ∼1–10 Myr. Moreover, our model also shows that high CO masses are not expected around FGK stars since their planetesimal discs are born with lower masses, explaining why shielded discs are only found around A stars. Finally, we hypothesize that the observed carbon cavities could be due to radiation pressure or accreting planets.