Do you use QListWidget or QListWidget inherited widget? If you inherit from listWidget and use mouse or drag events and didn't pass event to QListWidget, drag and drop will not work.
I made it with Qt Designer and I changed the drag and drop properties a lot, but now I changed them back to just dragDropMode = internalMove and put the others back to default. The selection mode is ExtendedSelection, but I tried the default, too.
That should work. I tried this with designer and could move the items in the preview mode (Ctrl-R/Cmd-R). That should work in the real code too, if you do not change other drag/drop settings there too.