  We present the results of a 10.5 yr, volume limited (28 Mpc) search for
supernova (SN) progenitor stars. We compile all SNe discovered within this
volume (132, of which 27% are type Ia) and determine the relative rates of each
sub-type from literature studies : II-P (59%), Ib/c (29%), IIb (5%), IIn (4%)
and II-L (3%). Twenty II-P SNe have high quality optical or near-IR
pre-explosion images that allow a meaningful search for the progenitor stars.
In five cases they are clearly red supergiants, one case is unconstrained, two
fall on compact coeval star clusters and the other twelve have no progenitor
detected. We review and update all the available data for the host galaxies
(distance, metallicity and extinction) and determine masses and upper mass
estimates using the STARS stellar evolutionary code and a single consistent
homogeneous method. A maximum likelihood calculation suggests that the minimum
stellar mass for a type II-P to form is m(min)=8.5 +1/-1.5 Msol and the maximum
mass for II-P progenitors is m(max)=16.5 +/- 1.5 Msol, assuming a Salpeter
initial mass function (in the range Gamma = -1.35 +0.3/-0.7). The minimum mass
is consistent with current estimates for white dwarf progenitor masses, but the
maximum mass does not appear consistent with massive star populations. Red
supergiants in the Local Group have masses up to 25Msol and the minimum mass to
produce a Wolf-Rayet star in single star evolution (between solar and LMC
metallicity) is similarly 25-30 Msol. We term this discrepancy the "red
supergiant problem" and speculate that these stars could have core masses high
enough to form black holes and SNe which are too faint to have been detected.
Low luminosity SNe with low 56Ni production seem to arise from explosions of
low mass progenitors near the mass threshold for core-collapse. (abridged).
