  Non divergence-free discretisations for the incompressible Stokes problem may
suffer from a lack of pressure-robustness characterised by large
discretisations errors due to irrotational forces in the momentum balance. This
paper argues that also divergence-free virtual element methods (VEM) on
polygonal meshes are not really pressure-robust as long as the right-hand side
is not discretised in a careful manner. To be able to evaluate the right-hand
side for the test functions, some explicit interpolation of the virtual test
functions is needed that can be evaluated pointwise everywhere. The standard
discretisation via an $L^2$-best approximation does not preserve the divergence
and so destroys the orthogonality between divergence-free test functions and
possibly eminent gradient forces in the right-hand side. To repair this
orthogonality and restore pressure-robustness another divergence-preserving
reconstruction is suggested based on Raviart-Thomas approximations on local
subtriangulations of the polygons. All findings are proven theoretically and
are demonstrated numerically in two dimensions. The construction is also
interesting for hybrid high-order methods on polygonal or polyhedral meshes.
