I coincidentally searched for these topics yesterday (tip: search by title only).
There are two topics:
last chance to see:
Last 'easy' chance to see:
First I'm copying Alan Lewis' post, next, I give some of my own suggestions and comments on this list that I know of (I am in now way monitoring all potential last chances worldwide, so feel free to add / update):
Alan's suggestions back in the days:
Asia: Jankowski's Bunting, Amani Woodcock, Okinawa Rail, Chinese Crested Tern, Cebu Flowerpecker, Jerdon's Courser, Baer's Pochard, Spoon-billed Sandpiper, Mindoro Bleeding-heart, Sangihe Shrike-thrush, Caerulean Paradise-flycatcher,
Africa: Madagascar Pochard (non re-intro), Sidamo Lark,
Pacific: Niau Kingfisher, Marianas Crow
Americas: Junin Grebe, Hooded Grebe, Cherry-throated Tanager (getting harder..), Alagoas F-G (retained as current sightings at one small forest patch only), Yellow-knobbed Currasow (TBC - by Chavez), Grenada Dove, Stressmann's Bristlefront,
my own comments:
Jankowski's Bunting, Chinese Crested Tern, Madagascar and Baer's Pochard, Spoon-billed Sandpiper, Niau (Tuomotu) Kingfisher, Junin and Hooded Grebe are slightly better off than some on this list that are in very serious (terminal) trouble (Jakowski's, CC Tern, Spoon-billed Sandpiper... were already discussed in the original topic).
I consider, from the list above and from own reading, Jerdon's Courser, Alagoas Foliage Gleaner, Stresemann's Bristlefront with no chances to see (anymore), and all of those are birds that haven been seen in the last 20 years (the Courser is the hardest to detect so it has a slightly better chance to survive undetected). Others that can be added to this 'probably exctinct but not officially declared as such' are Bahama Nuthatch, Cozumel Thrasher,...
Next, we have a 'realistic' last chance to see category (but hurry and/or be very lucky): Cebu Flowerpecker, Cherry-throated Tanager, Alagoas Antwren (not on the list above) and akikiki, 'akeke'e, kiwikiu and 'ākohekohe are almost extinct, if not functionally extinct (population size too low, treats to hard to counter). Last counts for the Tanager didn't get more than 9+6, the Antwren count was 6... The Tanager and Antwren can still be realistically seen, but it's really last chance for the Antwren, and while the Tanager can cling on, it's in dire straits. I have mixed feelings about Cebu Flowerpecker: the bird hasn't been photographed and there are no verified sightings in the last couple of years, so either there are no serious attempts to see it by people who report it widely, or it is simply not seen anymore. The Hawaiian Honeycreepers will go extinct pretty soon, and while I know the treats are complicated to tackle (Avian Malaria), I'm sorry to say, but those names don't attract attention of a greater audience to try and save them. Another addition to this paragraph may be Chilean Woodstar (won't survive for long).
Birds that are numbering just slightly more (and some could be placed in the paragraph above), but declining / very vulnerable are e.g. White-bellied Heron, Mariana Crow, the Sangihe birds, Botha's/Beesley's Lark, Masked Finfoot (Bangladesh and maybe Cambodia but very thin on the ground, or better: on the muddy banks and in the water), Vietnamese Crested Argus and Mindoro Bleeding-heart (I hope these ones are just hard to reach, wherever they still occur), Juan Fernandez Firecrown (cats...!),...
There are also some enigmas that could be still rather numerous, but have slipped off the radar as their traditional stake-out seems to be without the bird, and there are either no alternative spots or those spots are hard to reach:
Gurney's Pitta and Rufous-headed Robin spring to mind... I hope those make some kind of 'come back' in terms of secured sites where habitat is protected and there is a good chance to see them.