Although I won't presume to understand the mathematics, there's a problem with the stability of highly-inclined orbits if there are other bodies close enough or massive enough to perturb the system, namely the Kozai mechanism.
In celestial mechanics, the Kozai mechanism, or the Lidov–Kozai
mechanism, is a perturbation of the orbit of a satellite by the
gravity of another body orbiting farther out, causing libration
(oscillation about a constant value) of the orbit's argument of
pericenter. As the orbit librates, there is a periodic exchange
between its inclination and its eccentricity. (...)
The Lidov-Kozai mechanism places restrictions on the orbits possible
within a system (...) if the orbit of a planet's moon is highly inclined to the planet's orbit, the eccentricity of the moon's orbit
will increase until, at closest approach, the moon is destroyed by
Of course this inclination is relative to the equator of the planet, not to the plane of its orbit around its star. But since you specified that the planet's axial tilt is a moderate one, I'm assuming "inclined with respect to the equator" implies "inclined with respect to the orbital plane". If the axial tilt is zero, then that would be a polar orbit.
I have no idea how much time it would take for the Kozai mechanism to destabilize a highly-inclined orbit.