This was a question that was circling my head for a while. I mean, where does it go? Some may say that it's on the stage... And it probably is. But, I want to give a creative answer. I don't have much evidence to go on this but, shut up this is my answer.

Firstly, let's see what rooms Toy Chica goes in at night. Chica goes to the following rooms: The Main Hall followed by, Party Room 4 and, then entering the Office through the left vent.

Now, from what we know, there are blind spots within the camera view. Here, I found this poorly done picture on Google!

Yeah... I know... But, we can make it work. As we can see and, from what we know, Toy Chica starts on the stage, then moves to the Main Hall (the hall with no red in it) and, then enters the left vent from Party Room 4.

Now, let's think about this. Chica could have lost her beak in the main party room. It is the room with the biggest blind spot. Or takes it off when she knows she's in your view and, reattaches it when she she's knows she's in a blind spot. But that seems very unlikely so, I'm just sticking to original thought and, saying she loses it in the Main Party room blind spot. Case closed.

Awwwwww! Toy Chica is still cute, even if she loses her beak.(I give full credit to the artist of this picture. Keep up the great work!)