This is not a camera clipping issue, because all other objects and the background behind them
are rendered properly.
As long as the object touches the edge of the screen, it disappears.
It is as if it has a property like “do not render the object at all when part of it is outside the screen”.
Try adding a couple of vertices to the mesh (no need for them to form a face, we don’t want them to be visible) and moving them a reasonable distance away from the actual mesh, that will enlarge the bounding box. AFAIK that should do the trick.
Yes it is armature related and the object has been scaled tool. It is the head of the character, a helmet.
The center is the center of mass and when the head disappears, the center of mass is inside the camera.