Very infrequently, the interface of the furnace will close when adding fuel to it. The most recent instance of this, I had a furnace with a hopper above and below it. Here are the steps I took that caused the problem.
1. Add 64 cobblestone to the furnace with a shift-click.
2. Add 36 cobblestone to the hopper above the furnace with shift-click
3. Add a lava bucket to the furnace with a shift-click.
Adding the lava bucket caused the furnace interface to immediately disappear without hitting Esc, and the exterior of the furnace indicated that it was in the process of cooking. I went back into the furnace interface. The materials that I had put in the furnace in steps 1 and 3 were gone, and the material slot was in the process of filling up with the cobblestone that had been placed in the hopper in step 2.
I have attached the compressed save directory. The furnace on the left still shows that it is cooking, even though there is no fuel and nothing is being processed. Hopefully there is still data in the state information of the furnace to indicate what went wrong.
Loosing a stack of cobblestone, a bucket, and a block of lava isn't a big deal, but I could see this being very frustrating if it were a stack of iron or gold ore.