When you're there, try and work out a wiring diagram, and get some photos of how things are connected.

If you can work out the activation signals to the VFD, see if they remain active when the spindle stops. There is the possibility that the controller is stopping the spindle when too high a speed is commanded, so knowing what the activation signal/speed set signal are doing narrows down to if it's a controller issue, or a VFD issue.