  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 H$_2$, 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. 2019 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 timescales, 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 onto 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 ($\alpha\sim0.1$),
indicating that gas is lost on timescales $\sim1-10$ 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 hypothesise that the observed carbon
cavities could be due to radiation pressure or accreting planets.
