ABSTRACT Dust is an essential ingredient of galaxies, determining the physical and chemical conditions in the interstellar medium. Several complementary observational evidences indicate that the cosmic dust mass density significantly drops from redshift z = 1 to z = 0. Clearly, and for the first time during cosmic evolution, dust must be destroyed more rapidly than it is formed. By considering the dust production/destruction processes acting in this cosmic time lapse, we find that the drop can be explained if dust is mainly destroyed by astration (49 per cent contribution in the fiducial case) and supernova (SN) shocks within galaxies (42 per cent). Our results further imply that on average each SN destroys only $M_{\mathrm{ d},\mathrm{ sn}} =0.45\, \mathrm{ M}_\odot$ of dust, i.e. 5–10 times less than usually assumed, with a hard upper limit of Md,sn < 3.0 M⊙ set by the available metal budget and maximal grain growth. The lower efficiency might be explained by effective shielding of dust against shock processing in pre-SN wind shells.