I have a simple mesh which behaves like it has a "rip" when using proportional edit.
This mesh has no vertex groups, constraints, modifiers, but moving a vertex with proportional editing highlights the problem - not all vertices "follow their orders". Only each separate half of the mesh reacts to proportional edit independently, depending on initial selection.
When I isolate this mesh to another file, the problem comes along with it. Here is the file https://www.dropbox.com/s/bc4etnzfg7knwg0/OddMesh.blend?dl=0