Hmm, that's a good question Dellena. Previously I could have a huge pile of cuttings gathered from around the worlds and could take them home and graft them all happily. At the moment I am only testing one cutting/graft at a time and so far this file has been fine with grafting. I also haven't attempted to graft onto basil as every time I do that grafting breaks.
Either way, something has changed as I definitely could graft a multiple cuttings only a week or so ago. So I'll try multiple cuttings at once and see what happens and post back later today.
Just a note on grafting onto basil. It looks like it doesn't work as the sim does the 'T-jump' and the cutting stays in the inventory but a day later the plant will have another plant growing on top of it like
here in Twinmum's picture. When that happens for me if I save and quit then sometimes my sims can graft again. Other times no matter what I do grafting just doesn't work in that game file again at all.