Context. There is a long-standing and large discrepancy between the timescale for dust formation around evolved stars and the rapid dust destruction timescale in interstellar shocks. Aims: We use our latest estimates for dust processing to re-evaluate the dust destruction efficiency in supernova triggered shock waves, estimate the dust lifetime, and calculate the emission and extinction from shocked dust. Methods: We modelled the sputtering and fragmentation of grains in interstellar shocks for shock velocities between 50 km s-1 and 200 km s-1. We constrained the dust destruction using our recent dust model. Finally, we coupled our code to the DustEM code in order to estimate the emission and extinction from the dust post-shock. Results: Carbonaceous grains are quickly destroyed, even in a 50 km s-1 shock, leading to a shorter lifetime than in previous studies. Silicate grains appear to be more resilient, but the new destruction lifetime that we find is similar to previous studies and short compared to the dust injection timescale. Conclusions: The calculated fraction of elements locked in grains is not compatible with the observed values and therefore implies the re-formation of dust in the dense regions of the interstellar medium. Better modelling of the silicate sputtering together with hydrodynamical simulations of interstellar shocks, appears to reduce the silicate destruction and may close the destruction-formation timescale gap. Appendices are available in electronic form at http://www.aanda.org
