Resetting stones on a sinking patio
While I'm not an expert, typically you can pull up slates, re-level the sand underneath them, and then re-lay them.

It is entirely possible that the slates were put on too-thin a layer of gravel and sand, and that the underlying soil has compressed a bit since they were laid.  This is different from erosion.

It is also possible that they were laid in order to promote drainage and avoid puddles.