That's a good idea! Haven't heard of the borax treatment before, but it is used to get rid of household insects so it stands to reason. In my mind anyway.
You should check their sleeping quarters, with a flashlight, at night. Pick the birds up and examine them after dark. Some mite infestations, they don't live on the birds, they act more like bedbugs... They reside in the coop and only attack at night.
Parasites would be far and away my first guess.