The dearth of dwarf galaxies in the local Universe is hard to reconcile with the large number of low-mass haloes expected within the concordance Λ cold dark matter (ΛCDM) paradigm. In this paper, we perform a systematic evaluation of the uncertainties affecting the measurement of dark matter halo abundance using galaxy kinematics. Using a large sample of dwarf galaxies with spatially resolved kinematics, we derive a correction to obtain the abundance of galaxies as a function of maximum circular velocity – a direct probe of halo mass – from the line-of-sight velocity function in the Local Volume. This method provides a direct means of comparing the predictions of theoretical models and simulations (including non-standard cosmologies and novel galaxy formation physics) to the observational constraints. The new ‘galactic Vmax’ function is steeper than the line-of-sight velocity function but still shallower than the theoretical CDM expectation, implying that unaccounted baryonic physics may be necessary to reduce the predicted abundance of galaxies. Using the galactic Vmax function, we investigate the theoretical effects of feedback-powered outflows and photoevaporation of gas due to reionization. At the 3σ confidence level, we find that feedback and reionization are not effective enough to reconcile the disagreement. In the case of maximum baryonic effects, the theoretical prediction still deviates significantly from the observations for Vmax < 60 km s−1. CDM predicts at least 1.8 times more galaxies with Vmax = 50 km s−1 and 2.5 times more than observed at 30 km s−1. Recent hydrodynamic simulations seem to resolve the discrepancy but disagree with the properties of observed galaxies with spatially resolved kinematics. This abundance problem might point to the need to modify cosmological predictions at small scales.