  We investigate quantum stability of the generalised Proca theories in curved
spacetime treating gravity as a dynamical field. To compute the quantum
gravitational corrections we evaluate divergent part of the effective action at
one loop level. We employ Vilkovisky-DeWitt formalism for this task which gives
us a gauge invariant and gauge condition independent effective action. It is
shown that the quantum corrections are suppressed by a UV cutoff parametrically
higher than the Proca mass if the coupling constants are restricted to lie in a
certain range. Furthermore it is shown that the quantum corrections remain
suppressed even at scales where classical non-linearities dominate over kinetic
terms allowing Vainshtein mechanism to work.
