I used the dragon egg in the End in survival, right clicking to get it to move off the portal. It showed movement particles towards the southwest as it disappeared, but it was absolutely nowhere to be found in that direction or any other despite residing on a large plain. The obsidian pillars do not have the egg on them either. I even tried going back through the portal, and it didn't show up anywhere near my spawn point. For all I can tell after an hour of searching everywhere, it has vanished.