The Milford Sound mountains are at low risk of collapsing during earthquakes mainly because they are composed of gneiss, a type of strong and stable metamorphic rock. This rock type provides structural strength and resistance against shaking during seismic events, reducing the likelihood of collapse despite the region's seismic activity from the nearby Alpine Fault.

The Alpine Fault is an active major fault responsible for earthquakes in the region, but the geological composition of the Milford Sound mountains helps prevent collapse during such events. Although the area can experience earthquakes and landslides, the presence of gneiss implies the mountains themselves are structurally resilient to collapsing.

Thus, it's the geological nature of the rock—specifically the durability and metamorphic properties of gneiss—that contributes to the low risk of mountain collapse during earthquakes in Milford Sound.