We present the results of a 10.5-yr, volume-limited (28-Mpc) search for supernova (SN) progenitor stars. In doing so we compile all SNe discovered within this volume (132, of which 27 per cent are Type Ia) and determine the relative rates of each subtype from literature studies. The core-collapse SNe break down into 59 per cent II-P and 29 per cent Ib/c, with the remainder being IIb (5 per cent), IIn (4 per cent) and II-L (3 per cent). There have been 20 II-P SNe with high-quality optical or near-infrared 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 and SN environments (distance, metallicity and extinction) and determine masses and upper mass estimates for these 20 progenitor stars 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 mmin= 8.5+1−1.5 M⊙ and the maximum mass for II-P progenitors is mmax= 16.5 ± 1.5 M⊙, assuming a Salpeter initial mass function holds for the progenitor population (in the range Γ=−1.35+0.3−0.7). The minimum mass is consistent with current estimates for the upper limit to white dwarf progenitor masses, but the maximum mass does not appear consistent with massive star populations in Local Group galaxies. Red supergiants in the Local Group have masses up to 25 M⊙ and the minimum mass to produce a Wolf–Rayet star in single star evolution (between solar and LMC metallicity) is similarly 25–30 M⊙. The reason we have not detected any high-mass red supergiant progenitors above 17 M⊙ is unclear, but we estimate that it is statistically significant at 2.4σ confidence. Two simple reasons for this could be that we have systematically underestimated the progenitor masses due to dust extinction or that stars between 17–25 M⊙ produce other kinds of SNe which are not II-P. We discuss these possibilities and find that neither provides a satisfactory solution. 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. We compare the 56Ni masses ejected in the SNe to the progenitor mass estimates and find that low-luminosity SNe with low 56Ni production are most likely to arise from explosions of low-mass progenitors near the mass threshold that can produce a core-collapse.