I'm back again (lol). It seems as though I'm not the only one experiencing what DerekL now calls the 'draggable-but-not-droppable' situation. Fortunately, it isn't as frequent as it previously was. Strangely, for most of the people facing the same issue its after they drag someone to the doctor from another floor— afterwards it stops working. For me, so far, I've only ran into this issue again when dragging to the doctors at my lowest floor (it isn't the lowest floor, as seen in the image).
I was going to mention that the issue only seemed to be present with those two doctors, however I discover later on that this seems to trigger the rest of the staff members to be undropped to. The rest of my doctors, which are much higher up don't seem to trigger this issue (as I mentioned earlier, I dragged an idol to one of the lower doctors; did not work, however I managed to drop her to the higher up doctors. But the issue returned).