  Measuring the collapse time of a binary neutron star merger remnant can
inform the physics of extreme matter and improve modelling of short gamma-ray
bursts and associated kilonova. The lifetime of the post-merger remnant
directly impacts the mechanisms available for the jet launch of short gamma-ray
bursts. We develop and test a method to measure the collapse time of
post-merger remnants. We show that for a GW170817-like event at
$\sim\!40\,$Mpc, a network of Einstein Telescope with Cosmic Explorer is
required to detect collapse times of $\sim\!10\,$ms. For a two-detector network
at A+ design sensitivity, post-merger remnants with collapse times of
$\sim\!10\,\mathrm{ms}$ must be $\lesssim 10\,$Mpc to be measureable. This
increases to $\sim\!18-26\,$Mpc if we include the proposed Neutron star Extreme
Matter Observatory (NEMO), increasing the effective volume by a factor of
$\sim\!30$.
