Birds can moult unevenly and if the moult is not complete in 4 to 6 weeks a bird is said to be “stuck in the moult”. When this occurs the bird looks sickly and stops singing and new feathers can be brittle and dull.
The most common cause is a poor or one-sided diet, which does not provide a wide range or variety of foods.
Having the bird in a cold or hot draft, or an un-seasonal sudden change in the weather, can cause a false moult, which is not a disaster but can make a bird unfit to be shown (watch the air conditioning or heating and when transporting birds to and from a show).
The best treatment is to increase the green foods such as Dandelion, Cabbage, Spinach, Buk Choy etc. and to provide some of the oily seeds such as Rape, Linseed & Maw. Rape being the most likely eaten of the three. Also some natural sunlight helps the bird to metabolise the vitamins.
Providing a bath daily can assist in shedding the old feathers.
You could also supplement their diet with a mineral & trace element supplement dissolved in water; obtainable from your pet supplier.