Welcome to the forums!
I'm sorry you are having problems with your chicks...
Can you post some pictures of those chicks?
There could be many reasons for the chicks to not develop normally.
When the parents aren't in top physical condition, the chicks may suffer the consequences, the same happens when breeding birds closely related.
And the fact that you said that even in previous clutches you had the same problem, that particular pair shouldn't have been put to breeding again.
Since you mention the chicks' feathers aren't growing properly, most likely they have French moult, this can be identified very early on while the chicks are still on the nest and especially when it is a severe case of French moult.
If this is the case, then your flock (the adult budgies) are all carrying the virus and passing it to the chicks. Unfortunately there is no cure for it, and it really is best to not breed birds that are carriers of French moult.
Be aware that this is just a possibility, the best thing to do is to take your chicks to an avian vet so that they are properly examined.