  We show that in optical clocks based on Rabi interrogation, both
laser-frequency and magnetic-field flicker ($1/f$) noise with zero mean can
lead to servo errors at the $10^{-18}$ level if the negative-detuning (red) and
positive-detuning (blue) sides of the transition are always probed in the same
order. This is due to the strong correlations of flicker noise in combination
with an imbalance in the response of the servo discriminator to positive and
negative differential frequency noise between the red- and blue-side probing.
This imbalance is particularly large for a normalized discriminator. We derive
an analytical expression for the servo error based on the correlation function
of the laser-frequency or magnetic-field noise and compare it to numerical
servo simulations to demonstrate how the error depends on the noise level,
servo parameters, and probing sequence. We also show that the servo error can
be avoided by normalizing the discriminator with a moving mean or by reversing
the red/blue probing order for every second servo cycle.
