Divide 2 has two modes: one that removes the segment and one that cuts the segment but does not remove it. QCAD remembers the last setting that was used.
You can check / uncheck this option in the tools options toolbar while the diide 2 tool is active (it is a good idea in general to keep an eye on this toolbar):
If you cannot see this toolbar, you might have accidentally closed it. Open it again with the menu: View - Toolbars - Tool Options