I don't think she meant it's peeling off rather the color itself coming off which unfortunetly happens when it's this type of dye. I agree though, if the actual paint is peeling it's no good at all.if 'paint' is peeling off, i would be very worried that it is even bird safe at all...
as everyone has said, bird dyes are either food colouring or non toxic natural plant dyes... none of which should peel at all....
if i was you i would remove it entirely!
yeah i would just let it age too, but if the lost colour bothers you, retouch with food colouring...I would not even retouch it and would just let it age. I don't think your baby will care if it is a little dull.