Once archived, if the folio is still available in the producer service, you should be be able to see it and click a "Download" button. (Assuming you have a valid wireless connection and your library updates successfully.)
If you cannot see it, that generally means there's an invalid article in the folio. An example of this would be that you have one landscape article and one portrait article. When the Content Viewer detects an invalid folio, it won't display it as downloadable.
I would suggest deleting your articles one at a time until you determine which one is the culprit.
I guess what I was asking is when you tap Archive in the Adobe Content Viewer on the iPad there is a pop-up that says "Are you sure you want to Archive?" and "This item will be removed from your device. You may download it again at anytime for free." But there is no option to do this within the iPad app! At least none that I can see.
I ended up creating a new folio with the same articles. It works now, but the archive function is not intuitive! It should work the same as when you archive magazines in the Newstand app. I mean, that's how people expect it to work. I guess in Adobe speak archive = delete!
Anyway, if you archive something it removes it from the app and you will not see a download button.