Gradually, over the next couple of years, I predict that the mainstream media and the general public will essentially abandon the "Ivory-bill rediscovery" story, and organizations like the USFWS/Aububon/The Nature Conservancy/etc will abandon it too. (The Birdforum/Lunatic Fringe crowd will continue to find tantalizing Ivory-bill evidence far into the future).
The chronology of United States Ivory-bill claims here provides some useful historical perspective.
The last major Ivory-bill hysteria in this country occurred in a few years surrounding 1970. In those years, we had the Dennis/Big Thicket (Texas) Ivory-bill excitement, the Agey/Heinzmann claims (Florida), the Lowery photos (Louisiana), and the Santee (South Carolina) claims. I don't think the chronological clustering of those high-profile events is any coincidence--recent, "credible" Ivory-bill reports no doubt inspired other Ivory-bill searchers to get far too enthusiastic when any sort of weak "evidence" was found.
I think it's interesting that following the early 1970s, a good quarter-century evidently passed without truly massive excitement about purported Ivory-bills in the US. By the mid-1970s, I think it's likely that interested people had a belly-full of recent, high-profile Ivory-bill "false dawns", and with that mindset, the usual fleeting glimpses and double-knockies just weren't very exciting any more.
By 1999, I think enough time had passed that our collective "false dawn" memories had faded somewhat. Thus, starting in 1999, Kulivan begat the 2002 Pearl River search, which begat Cornell/Arkansas in 2004, which begat Auburn/Florida in 2005.
By now, I think people are again getting a belly-full of false dawns. When upcoming search seasons in Florida (and everywhere else) yield more goose eggs (and deer bleats, and maybe branch stubs), an ever-larger proportion of the public will tune out.
In some ways, I think periods of "Ivory-bill hysteria" can be compared to some historical financial hysterias (ie bubbles). Both types of hysteria can last a long time, but when they finally burst, it's in the collective memory for a long time, and the hysterical peaks are not reached again soon (if ever).
After this current Ivory-bill hysteria fades into the rear-view mirror, I think we'll be facing a very long period of general public/media disinterest in flimsy Ivory-bill rediscovery claims. Two or three decades from now, maybe the general public will once again be ready for another round of belief.