Long Intervals are when the Red Star doesn't pass close enough to Pern to drop Thread on the planet. Four hundred years pass without any Thread. The Ninth Pass comes immediately after a Long Interval, and at the end of the before-mentioned Long Interval, many believed Thread would no longer come back, but it did.
It is later revealed that Long Intervals happened when Ruth and Jaxom take the engines of the colony ships back in time and explode them inside a huge rift on the planet. The third engine is supposed to alter the Red Star's course enough that it'll never pass close enough again after the end of the Ninth Pass.