make sure that nothing interrupts the mother from her hatching duties. In order for eggs to hatch, the mother needs to be able to sit on them without having a dwarf step onto her nestbox square. In my experience, if a dwarf so much as walks over the nest the mother will continue to sit but the eggs will never hatch.
This challenge is compounded by the fact that in order to remove dud eggs, the dwarf must step onto the nestbox square. The mother is ready to lay more eggs a few months after the previous set were laid, so she is probably ready and then some when you decide you have duds. The dwarf steps into her nest, gets the duds, and she lays the new - which get 'broken' instantly because the dwarf is standing there, but she continues to sit. The dwarf goes away with the old duds and you hopefully watch the new duds, likely repeating the process for a while before you catch onto this icky game. ( I discovered this pattern when I wondered why my ankylosaurs were only able to hatch their first litters - when I set my dwarves to lead the babies away they were usually stepping into the nest at some point - removed that from happening and started to get a LOT more successful nests). I've had some nests hatch well that I totally ignored, but where there were many baby animals around - so animals stepping into a nest clearly wont break the eggs, but keep those dwarves away or else.
The way to break this double-dud clutching is to remove both sets of eggs and give Mom enough time to be ready to lay a hopefully fertile third batch, or else lead Mom away and cage her, clear the nest, then release her and let her do her thing.
Two other things that appear to break eggs - attempting to train Mom into a warbeast (this is an issue with ankylosaurs, but probably not parrots) - or moving Mom off of the nest for any reason (if you do that she likely wont try to go back on until she's ready to lay again.