Why do Moon's invisible periods differ from the Sun's six-month cycle at the poles?

The Moon has a much faster orbital period causing its declination to change relatively quickly.

The Sun's long period of six months of daylight followed by six months of darkness at the poles is tied directly to the Earth’s annual revolution around the Sun and its resulting axial tilt relative to the Sun. In contrast, the Moon orbits the Earth much faster. Because the Moon's orbital path constantly changes its declination relative to the celestial equator over a much shorter timescale—related to its roughly $29.5$-day synodic period—the duration during which its path remains entirely below the polar horizon is significantly shorter than the Sun’s yearly cycle. While the Sun stays high or low for months, the Moon cycles through periods of visibility and absence over a timeframe related to its own orbit.