I know this thread is well over a decade old at this point... BUT! I just found a solution! I was super worried about my bird not coming back, and I even tried saving and closing the game and then reloading the save, like suggested.
If you're like me, and came across this thread years later in search for a solution, here's a potential fix.
What I did was:
1) Enable testing cheats by changing the 0 to 1 in Commands.ini in EA Games\The Sims Medieval\GameData\Shared\NonPackaged\Ini
2) Place a bird cage furniture object, and assign the problem bird in question
3) Hold Shift + Left Click on the cage, click object..., and then Force Reset
Your bird *should* then come back to your shoulder. Hope this helps!