[ars]

It's not the day/night length.

It's the angle of the earth relative to the orbit of the moon. It's a geosynchronous orbit, so it must match the equator, including the angle.

Presumably in other months the angle of the moon's orbit (relative to the equator) is wrong for using this maneuver.

[btilly]

There are 3 bodies here, the Earth, the Moon and the Sun.

During the equinox the equator of the Earth lines up with the Sun-Earth axis. I can see that being significant in all sorts of ways. At other times of year, in a complicated maneuver, the Sun is going to pull the satellite off of that plane of orbit.