In vortex-dominated flows at high Reynolds numbers, vortex filaments interact with each other and reveal coherent geometrical structures, possibly persisting over long time scales. The force balance between the material velocity time derivative and the pressure gradient leads to complicated pressure gradients, which have to be handled accurately by the space discretization. It is argued that pressure-robust solvers are needed for long-time simulations of vortex dominated flows at high Reynolds numbers. Numerical benchmarks support the theory.