In many cases, they didn't. It's a common archaeological trope that if you visit a Norman Cathedral, you can safely ask when, not if the tower collapsed. Two prime examples are the Temple Church in Bristol and Winchester Cathedral.

Temple Church in Bristol was begun in the 14th Century as an expansion of a Knights Templar round church on a site near the River Avon. The site today is famous for its tower which lists at an alarming degree. This is because the tower is far too heavy for the ground it is built on. After every expansion, the builders had to wait - in some cases up to a decade - for the tower to stop subsiding so they could add the next level to it.

Winchester Cathedral is built on land between two rivers and is historically prone to subsidance. As a result, almost none of the 'straight' lines inside are actually parallel or perpendicular. In the late nineteenth century the situation became so dire that divers in breathing apparatus had to burrow down into the floodplane to retroactively add concrete foundations to the building to stop it entirely collapsing.