Roughly speaking, the system has stable configurations where the free magnetic energy $W_{\rm mag}$ assumes a strict local minimum.

That local minimum of $W_{\rm mag}$ is assumed where the combined permeance of the magnet and the iron plate has a strict local maximum.

Symmetry, is not always a valid argument in this regard. E.g., assume a circular iron ring with a hole that is larger than the magnet. Then the central position of the magnet (i.e., magnet in hole) will not be a local maximum of combined permeance. It will be a local minimum. That means the central configuration will be an equilibrium, but an *unstable* one.