  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
$\Lambda$CDM paradigm. In this paper we perform a systematic evaluation of the
uncertainties affecting the measurement of DM halo abundance using galaxy
kinematics. Using a large sample of dwarf galaxies with spatially resolved
kinematic data we derive a correction to obtain the observed abundance of
galaxies as a function of their halo maximum circular velocity from the
line-of-sight velocity function in the Local Volume. This estimate provides a
direct means of comparing the predictions of theoretical models and simulations
(including nonstandard cosmologies and novel galaxy formation physics) to the
observational constraints. The new "galactic $V_{max}$" function is steeper
than the line-of-sight velocity function but still shallower than the
theoretical CDM expectation, showing that some unaccounted physical process is
necessary to reduce the abundance of galaxies and/or drastically modify their
density profiles compared to CDM haloes. Using this new galactic $V_{max}$
function, we investigate the viability of baryonic solutions such as
feedback-powered outflows and photoevaporation of gas from an ionising
radiation background. At the 3-$\sigma$ confidence level neither energetic
feedback nor photoevaporation are effective enough to reconcile the
disagreement. In the case of maximum baryonic effects, the theoretical estimate
still deviates significantly from the observations for $V_{max} < 60$ km/s. CDM
predicts at least 1.8 times more galaxies with $V_{max} = 50$ km/s and 2.5
times more than observed at $30$ km/s. Recent hydrodynamic simulations seem to
resolve the discrepancy but disagree with the properties of observed galaxies
with resolved kinematics. (abridged)
