This certainly isn't a new problem. But it feels like the degree to which donors are getting fed up with the volume of appeals they receive is reaching a critical point -- not too surprisingly, as the amount of information we all receive via traditional as well as social media has gone beyond overwhelming. And I suspect that nonprofits who wait around for this to be confirmed by a major study may lose out. (Or maybe there's already been a major study, but my Google search failed to turn it up.)
It's a tough situation, because building a mailing list is a crucial task for a nonprofit. One-time donations are usually small and don't get you very far. The goal is to inspire repeat donations, hopefully of increasing size, from donors who've gotten to know your work and with whom you build an increasingly close relationship. But to do that, you've got to know who they are and how to reach them.
Okay, so how to combat this donor fed-up-ness? Unfortunately, the only answer that makes sense is to not only acknowledge the issue, but offer donors who want to opt out of your mailing list the opportunity to do so. You've probably heard this advice before, but I still don't notice many nonprofits who implement it -- or implement is successfully. (I've been trying to get off the appeals-mailing list of a major environmental organization for months now.)
This is where the wide array of communication methods can be your friend. You can offer people who make a one-time donation the opportunity to receive your newsletter, your email updates about news issues relevant to your work, or other substantive communications. Some will realize that they're interested enough to say yes. (Some of the others, you probably weren't interested in anyway -- for example, the aunts and uncles who sponsored the walkathon out of family loyalty, and would never donate to your cause otherwise.) If your content is interesting, and your messages are powerful enough, the recipients will step up and start making donations without receiving a traditional appeal.