The alignment of the Earth, moon, and the Sun is the reason why lunar eclipses do not happen more often. The orbit of the moon and earth are always tilted five degrees. This can be in either a horizontal or vertical direction. The only reason why a lunar eclipse does happen is that the moon, earth, and sun happen to be aligned.
This alignment can also cause a solar eclipse to occur. The earth sees it as the moon alternating around the path of the Sun. When full moons occur, we are unable to see the eclipses, because the moon is either north or south in direction to the sun.
The reason that we don't have solar and lunar eclipses every month is that the earth and moon's orbit is always tilted five degrees in a vertical or horizontal direction. The moon, sun, and earth are not aligned. When they are aligned, it causes a lunar or solar eclipse. From the earth's view, the moon alternates around the sun's path.
During the majority of full moons, the moon is either North or South of the sun, and we cannot see an eclipse. For this to occur, new and full moons must happen when the moon crosses the Ecliptic. Also, the intersection of the moon and earth orbital planes must align with both the earth-moon and sun-earth directions.