This may only happen after placing a number of fireplaces or furnaces on a single persistant server.
I currently placed 7 normal (visible) furnaces (fireplaces upgraded with stones) over the course of 5 days. I may have had a few others previously, but they APPEAR to have despawned over time.
While these 7 fireplaces are present, my next two attempts at placing fireplaces are invisible. They are invisible in both the fireplace and furnace state. If I am standing near, I can still access them via the inventory screen. And if I can remember where I put them, I can find them again. However, there is no visible clue that they are in the area. (These are not near any buildings. Open forest area).