The conclusions from Fontana's research -- at least as of several months ago, since they are probably still in development -- are summarized in an hour-long talk he gave at the Linux Collaboration Summit in April 2012, entitled, "The Decline of the GPL and What to Do About It." This talk is available as an episode in Bradley Kuhn and Karen Sandler's "Free As In Freedom" podcast.
About half the talk is devoted to answering the question of when the GPL was first assumed to be dominant. Asserting that "the rise of the GPL is inseparable from the rise of the Linux kernel" -- one of the first major projects to adopt it -- Fontana suggests that the assumption was firmly in place by 2002, and began to be questioned in the last seven years. How true the assumption was at any given period is a question he mostly ignores.
Examining various assertions about the GPL's decline and their methodologies, Fontana concludes that "even if there is a decline in the GPL, it must be very slight" but admits that "we don't actually know what's going on." However, he apparently thinks that the possibility is all too likely, because he speculates extensively about what the reasons for such a decline might be.
One possible reason is the increase of web developers, writing for cloud services that prefer to keep their software proprietary. Another may be that dual-licensing, in which software is available with both a copyleft license and a more restrictive or even a proprietary license, is now perceived as more cumbersome than permissive licenses.
However, Fontana suspects that the greatest reason may be the increased complexity added by GPLv3. According to Fontana, Eben Moglen justified GPLv3's increased complexity as an unavoidable necessity. He paraphrases Moglen as saying "The BSD license is simple because it doesn't do anything" -- but then adds on his own account, "But I think that GPLv3 goes too far in the other direction."
In Fontana's account, the GPLv2's complexity was manageable because, in the past, the Free Software Foundation in general and its founder Richard Stallman in particular used to spend considerable time online interpreting GPL licenses for developers. The result was a broad consensus about what the license meant.
The trouble is that, since GPLv3, much less of this interpretation has been done. Instead, interpreting licenses has been turned over to lawyers and other experts. Fontana acknowledges his own pleasure in being one of those experts. But he admits that the fact that GPLv3 is less readily understandable than BSD style licenses might have contributed to any decline in its use. Developers, he suggests, want to pick a license without having to wade through legal language or relying on experts.
One possible solution may be the one used by Creative Commons licenses: A so-called human-readable version of each license that gives its essentials in clear language, backed by a longer, more complex legal version. But the solution that Fontana seems to favor is a license that is more clearly written to start with, backed by an authority in how to interpret it.
Fontana acknowledges that the Free Software Foundation probably disagrees with him, and that his suggestion is "unorthodox." Perhaps that is the reason he prefers to downplay Copyleft.next.
However, to judge from Fontana's posts on Identi.ca, so far as Copyleft.next has any clear goals -- which is debatable -- it seems intended as an effort to produce a clearer version of GPLv3. "I would like to try to make #GPL.next shorter, simpler, easier to understand, if possible," he writes in one post, and "I'm thinking of replacing 'Program' with 'Work' to emphasize that license can be used for non-software."