  Previous studies have shown that planets that rotate retrograde (backwards
with respect to their orbital motion) generally experience less severe
obliquity variations than those that rotate prograde (the same direction as
their orbital motion). Here we examine retrograde-rotating planets on eccentric
orbits and find a previously unknown secular spin-orbit resonance that can
drive significant obliquity variations. This resonance occurs when the
frequency of the planet's rotation axis precession becomes commensurate with an
orbital eigenfrequency of the planetary system. The planet's eccentricity
enables a participating orbital frequency through an interaction in which the
apsidal precession of the planet's orbit causes a cyclic nutation of the
planet's orbital angular momentum vector. The resulting orbital frequency
follows the relationship $f = 2 \dot{\varpi} - \dot{\Omega}$, where
$\dot{\varpi}$ and $\dot{\Omega}$ are the rates of the planet's changing
longitude of periapsis and ascending node, respectively. We test this mechanism
by simulating cases of a simple Earth-Jupiter system, and confirm the predicted
resonance. Over the course of 100 Myr, the test Earths with rotation axis
precession rates near the predicted resonant frequency experienced pronounced
obliquity variations of order $10^\circ$-$30^\circ$. These variations can be
significant, and suggest that while retrograde rotation is a stabilizing
influence most of the time, retrograde rotators can experience large obliquity
variations if they are on eccentric orbits and enter this spin-orbit resonance.
