I'm certainly in favor of digital archiving, and I'm not aware of many arguments against it. One argument that does come to mind comes (I believe) from one of the essays in Antoinette Burton's edited volume Archive Stories. The essay included a story about the Google books digitization project. The author had previously read the print version of a book, on which the publisher had posted a post-it-like sticker on a portion of text that some governing authority found objectionable. The thing was that readers could easily remove the sticker and read the text underneath. The author was considering using the story behind that sticker as an introduction to a written piece, and out of curiosity checked the digitized version -- in which Google had apparently removed the sticker for scanning and then possibly thrown it away.

That's a subtle point, but it is important. Archives are, by their nature, already mediated before the historian gets to them -- often by many people with conscious or unconscious agendas. Digitization can operate as another layer of mediation, obscuring small but potentially meaningful pieces of information from researchers. As I said, I'm still a big fan, but it is worth approaching this critically.

Researcher at the US National Archives here. Different facilities have a bit different philosophy, but the textural records division at College Park ( essentially the main, headquarters branch) has a dislike of digital copies if it means separating pages that have been bound or stapled. One can see their point to a certain extent as they are trying to prevent individual sheets from being misplaced or shuffled, but at the same point they are applying this with a broad brush and expecting that researchers somewhat fold a document that may be printed on extremely fragile paper in order to get a good quality copy. I've argued with the interns who staff the assistance desks over this and sometimes win, but often don't.

In a perfect world everything would be professionally digitized and the originals stored away, but we don't have the budget for that.

The drawback to digitizing materials (or transferring them in some other way to another medium) is that the originals are often then lost or thrown away. I ran into this doing research for my thesis -- my university library houses our state historical society, which has a large and very comprehensive newspaper library. Unfortunately, the library sometime in the 1960s started putting newspapers on microfilm or microfiche, and then destroying the originals, on the theory that the microfilm would last forever.

Well, fast forward to the 2000s when I was thesis-ing, and the microfilm had suffered from several generations of people passing it through viewing devices -- dust and debris gets into the film, the viewing machines sometimes scratch or tear a roll, people mishandle or misfile the film, film is patched with cellophane tape -- and you can see the problems we run into with data loss. As /u/SnarkMasterRay says elsewhere in this thread, the ideal situation would be to digitize AND store the originals, but many archives don't have the space or money to do that.

Another issue to consider is that digital storage suffers from decay in the same way that print storage does. Digital storage is a fairly new medium (it's actually a collation of many kinds of media), but tape, optical storage (CDs/DVDs) and hard drives all degrade over time. Standards for the type of media also vary wildly -- do we keep pdfs of a printed page, to preserve the design, or convert everything to plain text using OCR, or try to do both? What about storage media that's incompatible with new technology? My wife recently found a set of cassette tapes of sermons her grandmother, a minister, had delivered; we have no cassette player but can likely procure one -- what if those were 8-tracks?