I have a small server of two people, both of us admins. Yesterday I found two parrots, a white and a cyan, tamed them, and tp'd back to my home. I made them sit in my home as i did a few things, logged in and out, and they were fine. Ended up finishing my home, setting respawn point, and cancelled the parrot's sit-action.

Today I logged on, and cyan was gone. I walked around to see if it would spawn from a distance - nope. Tp'd to a location and back, still no. Back to home, walked a distance and summoned new parrots until I got a cyan, tamed it. Walked back home, did a few things there, logged off.

This evening I logged in again, both parrots there. Walk to other side of home and notice cyan is gone. I see white flying towards me and disappear once it reached my avatar. Open menu and there's no parrot on shoulder. I walk a distance again and no parrots. Tp to a different location and back and still no parrots.

ETA: When I summoned the new parrots I ended up summoning one into my home. This untamed parrot seems to be unaffected emotionally or physically by the disappearances.