Abstract : Context. In the context of planet formation, anticyclonic vortices have recently received much attention for the role they can play in planetesimal formation. Radial migration of intermediate-size solids towards the central star may prevent them from growing to larger solid grains. On the other hand, vortices can trap the dust and accelerate this growth, counteracting fast radial transport. Several effects have been shown to affect this scenario, such as vortex migration or decay. Aims: We aim to study the formation of vortices by the Rossby wave instability and their long-term evolution in a full three-dimensional (3D) protoplanetary disc. Methods: We used a robust numerical scheme combined with adaptive mesh refinement in cylindrical coordinates, which allowed us to affordably compute long-term 3D evolutions. We considered a full disc radially and vertically stratified, in which vortices can be formed by the Rossby wave instability. Results: We show that the 3D Rossby vortices grow and survive over hundreds of years without migration. The localised overdensity that initiated the instability and vortex formation survives the growth of the Rossby wave instability for very long times. When the vortices are no longer sustained by the Rossby wave instability, their shape changes towards more elliptical vortices. This allows them to survive shear-driven destruction, but they may be prone to elliptical instability and slow decay. Conclusions: When the conditions for growing Rossby-wave-related instabilities are maintained in the disc, large-scale vortices can survive over very long timescales and may be able to concentrate solids.