What specific rotational characteristic causes the shadows cast by crater rims near the South Pole to be stable?

The Moon’s axis of rotation is tilted only about $1.5^ ext{ degrees}$ relative to its orbital plane.

The persistence and stability of the deep shadows in the lunar South Pole region are directly attributable to the minimal tilt of the Moon's rotational axis relative to the plane of its orbit around Earth. This tilt is remarkably small, being only about $1.5^ ext{ degrees}$. Because the axis is nearly perpendicular to the orbital plane, the Sun always appears very low on the horizon when viewed from the polar regions. This low angle means that any elevation, such as a crater rim, casts an incredibly long, sharp, and stable shadow that rarely shifts position over the course of a lunar day or year, thus maintaining the near-total darkness required for trapping volatiles.