  We study the orbital stability of a non-zero mass, close-in circular orbit
planet around an eccentric orbit binary for various initial values of the
binary eccentricity, binary mass fraction, planet mass, planet semi--major
axis, and planet inclination by means of numerical simulations that cover $5
\times 10^4$ binary orbits. For small binary eccentricity, the stable orbits
that extend closest to the binary (most stable orbits) are nearly retrograde
and circulating. For high binary eccentricity, the most stable orbits are
highly inclined and librate near the so-called generalised polar orbit which is
a stationary orbit that is fixed in the frame of the binary orbit. For more
extreme mass ratio binaries, there is a greater variation in the size of the
stability region (defined by initial orbital radius and inclination) with
planet mass and initial inclination, especially for low binary eccentricity.
For low binary eccentricity, inclined planet orbits may be unstable even at
large orbital radii (separation $> 5 \,a_{\rm b}$). The escape time for an
unstable planet is generally shorter around an equal mass binary compared with
an unequal mass binary. Our results have implications for circumbinary planet
formation and evolution and will be helpful for understanding future
circumbinary planet observations.
