  Taking the standard parametrization of three-flavor neutrino mixing, we
carefully examine the evolution of three CP-violating phases $(\delta,
\alpha^{}_1, \alpha^{}_2)$ with energy scales in the realistic limit
$\theta^{}_{13} \to 0$. If $m^{}_3$ vanishes, we find that the one-loop
renormalization-group equation (RGE) of $\delta$ does not diverge and its
running has no quasi-fixed point. When $m^{}_3 \neq 0$ holds, we show that the
continuity condition derived by Antusch {\it et al} is always valid, no matter
whether the $\tau$-dominance approximation is taken or not. The RGE running of
$\delta$ undergoes a quasi-fixed point determined by a nontrivial input of
$\alpha^{}_2$ in the limit $m^{}_1 \to 0$. If three neutrino masses are nearly
degenerate, it is also possible to arrive at a quasi-fixed point in the RGE
evolution of $\delta$ from the electroweak scale to the seesaw scale or vice
versa. Furthermore, the continuity condition and the quasi-fixed point of
CP-violating phases in another useful parametrization are briefly discussed.
