<p><i>Chromonics</i> are special classes of nematic liquid crystals, for which a <i>quartic</i> elastic theory seems to be more appropriate than the classical quadratic Oseen–Frank theory. The relaxation dynamics of twist director profiles are known to develop a shock wave in finite time in the inviscid case, where dissipation is neglected. This paper studies the dissipative case. We give a sufficient criterion for the formation of shocks in the presence of dissipation, and we estimate the critical time at which these singularities develop. Both criterion and estimate depend on the initial director profile. We put our theory to the test on a class of initial <i>kink</i> profiles, and we show how accurate our estimates are by comparing them to the outcomes of numerical solutions.</p>