Confirmed affecting players on Realms, even the owner playing alone. Tested on Windows 10 Beta. Maybe the title should be updated to reflect it's not a LAN only issue?
Also happened to me, at version 0.15.0, using realms in survival mode. It was a double chest and when I broke the right half the items didn't drop, effectively destroying that half's content.
Later I couldn't reproduce the bug.
This happens when you place any item while aiming at the fence, not only on the top. Completely reproducible, allows reproduction of all items tested so far.