If we say "Recently I have been ill", I think "recently" is used to modify the whole sentence. If we say "I have been ill recently", I think "recently" is also used to modify the whole sentence. But if we say "I have been recently ill", it seems to me that "recently" is modifying the word "ill" only. So if we want to have "recently" to modify the whole sentence, apparently we do, we probably would use "recently" at the end of the sentence. I am not sure this is correct. But just for your reference. Hope others will provide more convincing answers.