I'm sorry to hear your finches are having this problem. There are several reasons that finches lose their feathers like this. The first thing to do is get rid of those mite cans. They are toxic to both your birds and you, and do more harm than good. They were designed to make money for pet stores, not to help birds. Treating for mites is not going to help, if the birds have, for example, a fungal infection. I recommend that you consult a bird vet to find out if there are physical problems. Vets have safe prescription medications. This link will help you find a vet:
Mites, lice, and other parasites can cause feather loss. If you examine a bird very carefully, you may be able to see these tiny bugs. Skin infections can also be to blame. If your finches are rubbing their heads on perches, cage bars, or anything else, that's a sign of itching. That could mean there's either an infection or a parasite. There are also internal parasites, such as worms or protozoans, that can cause feather loss. A few diseases do, too. If you suspect any of these things, you take can one bird to a vet for examination and diagnosis, then tell the vet you need to treat your whole flock.
Nutritional deficiencies can also lead to feather loss. Many commercial finch seed mixes are not adequate, and it's a good idea to add some fresh foods. Eggs are especially useful when birds are losing feathers. Try giving your finches some mashed boiled egg with the crushed shell.You can add a few pieces of finely chopped green vegetables such as cucumber and cabbage. It would be best to switch to a pelleted food, rather than seeds.
Finches need full-spectrum lighting (like the sun) every day in order to produce vitamin D in their bodies. Sunlight coming through a window doesn't work because the glass filters out some of the important rays. Without enough vitamin D, the finches can't utilize calcium properly, and feather loss on the head is one of the first signs. You can buy full spectrum lights in most home improvement stores. If you live in a warm southern climate, you can set their cage outside in the sun for an hour or so, but watch carefully to be sure they don't get overheated and that no predators bother them.
Finally, sometimes finches will pluck out each other's head feathers. I think you'd see them if this were going on, but I thought I'd mention it, just in case.
If you have more questions, just let me know. I hope your finches soon grow new feathers.
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