  Systems with spin-orbit coupling do not conserve "bare" spin current
$\bf{j}$. A recent proposal for a conserved spin current $\bf{J}$ [J. Shi {\it
et.al} Phys. Rev. Lett. {\bf 96}, 076604 (2006)] does not flow persistently in
equilibrium. We suggest another conserved spin current $\bar{\bf{J}}$ that may
flow persistently in equilibrium. We give two arguments for the instability of
persistent current of the form $\bf{J}$: one based on the equations of motions
and another based on a variational construction using Lieb-Schulz-Mattis twist
operators. In the absence of spin-orbit coupling, the three forms of spin
current coincide.
