Downloaded the project and this was the problem:
You need to check that box to ensure that it doesn’t occlude the SkinnedMeshRenderer when the camera gets too close, I can’t say for sure what unity is using to determine that the object needs to be culled, since at least some part of the SkinnedMeshRenderer is still within the frustum so it doesn’t make a lot of sense, but that’s definitely the cause.
Keep in mind that these particular models have a ton of transforms which are it’s bones, and the SkinnedMeshRenderer appears to be buried down in Object_8.