bald finch

Question
one of my female zebra finch has got a bald bum, what's wrong
with her? she is in a cage with a male finch they have been
together since they were born about 4 months now. they keep
trying to breed but nothing happens

Answer
Sounds like she is either picking at her own rump or the male is. Keep a close eye on them and see who's doing it. To help discourage feather picking, you can buy some sour tasting spray from pet stores to spray onto the feathers. This is only to be done if the female is picking at herself. If it's the male, he's trying to get her to breed and she doesn't want to.
They are also too young to have babies. My zebras don't usually start laying until they are 5 mos. However, I I also try to discourage breeding in finches under 1 year old. They are too young and will not know how to care for the babies.