The bug
When you start flying with a parrot on your shoulder, it will disappear when flying up.
Steps to reproduce
Spawn and tame a parrot
Go into creative mode
Allow the parrot to land on your shoulder
Start to fly
Fly up and notice the parrot disappears
Linked issues
is duplicated by
relates to
Comments
so, yes they vanish when you fly up, but try to land on the gound after the have vanished and then jump, they magicly reapear
Also just happened for me, short video showing the behaviour here:
[media]
I'm not sure, but shouldn't it rather say "parrots don't render" rather than "disappearing"?
Theyare still there (see video towards the end), just not rendering.
As soon as the player picked them up, they seem to have become "part of the player" (their hitbox is non-existent anymore and they cannot be found anymore via entitydata {}).
That the parrots are still "attached" on the player, just not rendering, can be tested with:
/testfor @p {ShoulderEntityLeft:{id:"minecraft:parrot"},ShoulderEntityRight:{id:"minecraft:parrot"}}
The same thing happens when you jump and hit your head on an upper-half slab (even in survival mode). Not sure whether this should be considered a separate issue.
you can carry multiple parrots and some of them can disappear as seen here: https://youtu.be/aGz8q8QgugA

i continued playing around with this glitch and it disappears for good after a few tries
Confirmed for 17w13b

Confirmed for 17w14a.
I also suggest a rename:
"Parrots on shoulders stop rendering when flying up in creative or spectator mode"

Actually, it should just be renamed to "Parrots on shoulders stop rendering when flying up in creative", due to the fact that parrots getting on your shoulders in spectator is also a bug in itself.
Not fixed in 17w15a.

#4 in the description under "How to Reproduce" needs to be updated since right-clicking no longer puts parrots on your shoulders.
Suggested change: "4. Allow the parrot to land on your shoulder"
Updated the description, thanks.

Parrots don't seem to land on your shoulders while flying anymore (exception is when they're already on your shoulder while flying from previous version). This honestly seems like a very odd way to try and fix something... they just tried to remove it altogether.
I just tried flying into the parrot with an elytra while the parrot was airborne and that allowed it to land on my shoulder (it's kind of finicky since the parrot dismounts if you start gliding upwards at all). I then double-tapped space to start flying which also disabled the elytra without making the parrot's model disappear. After that I was able to reproduce the bug like before.
So... fixed/not really though? Idk, this is just weird now.
Whoever was in charge of fixing this did it both badly, and in a horrible way (they both failed to fully remove a feature, and shouldn't be removing features to begin with).
As a side note, descending doesn't make the parrot's model disappear, only ascending. Also, the initial jump causes the parrot to dismount, which is why step 3 was start flying and step 4 was allow parrot to land on shoulder.

Okay, it turns out a much simpler way is to fall into an airborne parrot to get it to land on your shoulder, then double-tapping space to start flying while still falling. The bug can then be reproduced from there.
Here's a couple examples on how to reproduce the bug in case what I said was too wordy (I just made these, so they're up-to-date):
Example 1: https://youtu.be/bHVC9VVirOg
Example 2: https://youtu.be/CgU5K8u4ZIk

In 17w16a, parrots now dismount your shoulder if you're in the air for even a split second (affects flying, jumping, walking down stairs, and any form of falling whatsoever).
This would probably be considered a new bug involving the fix, but... Can this really be called a fix? I'm more than disappointed in the amount of effort being put into fixing this bug. I mean, couldn't they just make double-tapping shift dismount the parrot or something? Why are they so set on completely removing this feature? And why are they so bad at removing it?
No, this is actually intended behavior.

Except for walking down stairs. There is no way that's intended behavior.
The rest of what I said still stands.
Disappear != go off, disappear = gone out of existence.