Disappearing Parrots

What I expected to happen was...:
The parrots would follow you anywhere on the map like tamed Dogs do.

What actually happened was...:
After going across an ocean, one disappeared completely. Wouldn't teleport to me when on land either. Went back and tamed 2 more, and disconnected and reconnected. They were no longer in the vicinity, and were not following.

Steps to Reproduce:
1. Tame Parrot in Jungle biome
2. Go across ocean, or disconnect from public LAN server.
3. Parrots will despawn.