We study resolution effects in numerical simulations of gas-rich and gas-poor major mergers, and show that the formation of slowly rotating elliptical galaxies often requires a resolution that is beyond the present-day standards to be properly modelled. Our sample of equal-mass merger models encompasses various masses and spatial resolutions, ranging from about 200 pc and 105 particles per component (stars, gas and dark matter), i.e. a gas mass resolution of ∼105 M⊙, typical of some recently published major merger simulations, to up to 32 pc and ∼103 M⊙ in simulations using 2.4 × 107 collisionless particles and 1.2 × 107 gas particles, among the highest resolutions reached so far for gas-rich major merger of massive disc galaxies. We find that the formation of fast-rotating early-type galaxies, that are flattened by a significant residual rotation, is overall correctly reproduced at all such resolutions. However, the formation of slow-rotating early-type galaxies, which have a low-residual angular momentum and are supported mostly by anisotropic velocity dispersions, is strongly resolution-dependent. The evacuation of angular momentum from the main stellar body is largely missed at standard resolution, and systems that should be slow rotators are then found to be fast rotators. The effect is most important for gas-rich mergers, but is also witnessed in mergers with an absent or modest gas component (0-10 per cent in mass). The effect is robust with respect to our initial conditions and interaction orbits, and originates in the physical treatment of the relaxation process during the coalescence of the galaxies. Our findings show that a high-enough resolution is required to accurately model the global properties of merger remnants and the evolution of their angular momentum. The role of gas-rich mergers of spiral galaxies in the formation of slow-rotating ellipticals may therefore have been underestimated. Moreover, the effect of gas in a galaxy merger is not limited to helping the survival/rebuilding of rotating disc components: at high resolution, gas actively participates in the relaxation process and the formation of slowly rotating stellar systems.