On my whitelisted server, I sometimes encounter an issue in which a furnace or campfire refuses to cook items, despite previously working. In such cases, I've found that moving the offending block to a new location fixes it... temporarily. This has been shown to affect all three types of furnace, and when I placed a chest or a different type of furnace where a "frozen" furnace was, I found that I could not open it. Otyher players on my server have encountered the same problem.