Sorry if my first response seemed a little curt. It's just that I see little value in labelling for the sake of labelling. I use 'adverbs of frequency' as a shorthand for always, usually, normally, frequently, often, sometimes, occasionally, hardly ever, rarely, seldom, never, etc when I am talking about the position of adverbs in a sentence, but I never ask learners to label adverbs.
No. Those would be adverbs such as 'often' or 'seldom'.
If you absolutely have to name an adverb type, you can make up the term 'reiterative adverb', and put "again" in that group (possibly as the only member of the group). However, though it's a temporal adverb, I don't believe there is any subclassification.