The observed signatures of winds from X-ray binaries are broadly consistent with thermal winds, driven by X-ray irradiation of the outer accretion disc. Thermal winds produce mass outflow rates that can exceed the accretion rate in the disc... We study the impact of this mass loss on the stability and lightcurves of X-ray binaries subject to the thermal-viscous instability, which drives their outbursts. Strong mass loss could shut off outbursts early, as proposed for the 2015 outburst of V404 Cyg. We use an analytical model for thermal (Compton) wind mass loss. Scattering in the strong wind expected of long Porb systems enhances the irradiation heating of the outer disc, keeping it stable against the thermal-viscous instability. This accounts very well for the existence of persistently bright systems with large discs such as Cyg X-2, 1E 1740.7-2942, or GRS 1758-258. Wind mass loss shortens the outburst, as expected, but insufficiently to explain the rapid decay timescale of black hole X-ray binary outbursts. However, varying irradiation due to scattering in the wind produces lightcurves with plateaus in long Porb systems like GRO J1655-40. Mass loss is not a major driver for the outburst dynamics up to luminosities 0.1-0.2 L_Edd. Higher luminosities may produce stronger mass loss but their study is complicated since the wind becomes opaque. Magnetic winds seem more promising to explain the fast decay timescales generically seen in black hole X-ray binaries. Thermal winds can play an important role in the outburst dynamics through the varying irradiation heating. This may be evidenced by relating changes in wind properties, X-ray spectra or luminosity, with changes in the optical emission that traces the outer disc. Simulations should enable more accurate estimates of the dependence of the irradiation onto the disc as a function of irradiation spectrum, radius and disc wind properties. (read more)