If you move far enough from a stacked entity to cause it to stop rendering, it will desynch from the entity it is riding until you save/quit/reload the world. I was only able to test this in Singleplayer, I don't know if it's an issue in multiplayer as well.

GIF of the bug: http://gfycat.com/SpeedyElectricDesertpupfish

Process to replicate:

/summon ArmorStand ~ ~1 ~ {CustomName:test,PersistenceRequired:1,NoGravity:1,Marker:1,Passengers:[{id:Villager,PersistenceRequired:1,NoAI:1,Silent:1}]}

Fly away until the Villager stops rendering, but the ArmorStand is still visible.

/tp @e[name=test] @p

The ArmorStand will appear instantly, but the Villager will either:
1) Still be rendered at the original position, if you moved close enough to it to make it visible again before running the tp command; or
2) Display after a second if you ran the tp command while the Villager was not in render distance. If you move and run the tp command again, the Villager will not come with the ArmorStand.

If you save and quit to title, and then reload the world, the Villager will once again become a passenger of the ArmorStand, and teleporting will work (so long as the Villager is within render distance).