Chika, there is no way to prevent that. At least not that I've found, but there are a couple not so great workarounds.
Essentially anything in the view that lines up with the "Break View" lines will be broken. There unfortunately is no way to exclude any parts from the break. In the past when I have had that situation the only ways I've gotten around it is to build my ISO View explode so that the geometry does not overlap in the X or Y Axis depending on which axis the break is needed. Additionally, you could use a different view (Top, Front or Side) rather than an Isometric to do the same type of thing where the parts do not overlap in the axis in question.
Not the answer you're looking for I'm sure ... Good luck with it
I actually suppressed that part (the one got cut) before I use Break view but it did not work when I unsuppressed it. Well I can use other views as you suggested. Thank you