AX J1745.6-2901 is a low-mass X-ray binary with an accreting neutron star, showing clear evidence for highly ionized absorption. Strong ionized Fe Kα and Kβ absorption lines are always observed during the soft state, whereas they disappear during the hard state. We computed photoionization stability curves for the hard and the soft states, under different assumptions on the adopted spectral energy distributions and the physical parameters of the plasma. We observe that the ionized absorber always lies on a stable branch of the photoionization stability curve during the soft state, while it becomes unstable during the hard state. This suggests that photoionization instability plays a key role in defining the observable properties of the ionized absorber. The same process might explain the disappearance of the high ionization absorber/wind during the hard state in other accreting neutron stars and black holes.