The time derivative of that expression is indeed zero.
Actually, if you think about it, the only plausible way you could have something in space with zero jerk and non-zero acceleration would be an interstellar ship maintaining constant acceleration, so the suggested rule is almost exactly wrong.
>a constant times the $-e_r/r^2$, and the time derivative of that is definitely not zero.
I don't see a term there that is time-dependent.