Character becomes detached from own collision capsule and sinks when moving over certain parts of terrain

My 3rd person character starts off moving over standard unity terrain without any issues:

However, when I walk over certain parts of the terrain only, the character starts to rapidly sink, until it has disappeared under the terrain. It doesn't fall however, since it seems the character has become separated from its collision capsule, which remains on the ground:

The character still runs around, but moves erratically left and right. This only happens in some areas of the terrain, like there are invisible holes. But it's strange that the collision remains on the surface. It doesn't appear to be related to the gradient of the terrain, since it happens on various slopes. Any ideas what's going on? (I am using an identical player controller on another level with no problems, so it doesn't appear to be settings on that).