I know this was answered a long time ago but maybe new people have the same question. I have seen 3 birds who have lost either there top or bottom beak. In all three cases plus one I heard about on a 'net forum, these birds were fed seed diets that were purchased at the grocery store.
There are two problems with this. First a seed diet is not healthy. Even if it had all the nutrients needed, birds will not get them all because like us they will only eat what they like and toss the seed they don't like.
Secondly and even more important, all bird foods that are bought in places that also sell groceries and have seeds in them have NO nutrients. The reason is raw seeds, which is what birds need, contain little critters like moth larvae, Weevils and the like. Since they do not want these bugs to get into other groceries and infest a food store, they cook the feed to kill them off. This also kills ALL the nutrients in the feed, thus the birds are severely malnourished and their beaks fall off. It is very sad.