After a charcoal burner or furnace has had multiple stacks dragged in and out of it, it seems to go in a bugged state where you are only able to drag items one at a time into its inventory slots.
Attempting to drag a stack into a bugged slot fails to remove anything from your inventory and makes it look like there is nothing in the bugged slot. Dragging a single item into the bugged slot that has been visually emptied brings back the items that were in it previously visually, but still does not allow for stacks to be dragged into it.
Resolved in [0.9.21]
Duplicate of This Report