Why don't eclipses happen every month?
The moon's orbit is tilted, so at most new and full moons it passes just above or below the line where an eclipse could happen. Eclipses need a coincidence, and coincidences don't keep a calendar.
Two things have to line up
Every month has a new moon and a full moon. Almost none of them produce an eclipse, because the moon is in the wrong place at the wrong height.
The moon is usually too high or too low
The moon's orbit is tilted about 5° from Earth's orbit around the sun. For most of each month the moon rides above or below the ecliptic, the flat plane Earth travels in. A new moon up there casts no shadow on us.
The moon has to be at a node
The moon's orbit crosses the ecliptic at exactly two points, the nodes. An eclipse happens only when the moon is at a node during a new moon (solar) or a full moon (lunar). Both conditions at once.
Follow the moon through one month
Most of the month
The moon rides above or below the dashed line. New moon comes and goes, full moon comes and goes, no eclipse. This is almost every month.
Twice per orbit
The moon crosses the ecliptic at a node. If that crossing lands on a new or full moon, you get an eclipse. If it lands on a quarter moon, nothing happens.
Over the years
The nodes themselves drift. The eclipse seasons slide across the calendar, which is why there's no simple monthly rule to memorize.
So why isn't it a tidy schedule?
The nodes don't stay put. The line connecting them slowly rotates, completing one full turn every 18.6 years. So the windows when the moon can eclipse drift through the calendar year.
Eclipses arrive in seasons, roughly twice a year, but the dates shift year to year. Over a long stretch they do repeat on an 18-year cycle called the Saros, but that's not a rhythm you'd notice month to month. That's exactly why it feels random.