Nothing is impossible. Impractical maybe.
I would suggest that there are many, many species impossible to house in captivity realistically. While husbandry is always advancing and we've learned a lot about caring for species once thought impossible, I do not see most deep sea fishes and larger oceanic species like the Blue Whale as ever being possible to keep.
Rodents are rarely kept, considering they make up 20% of all mammals and, like amphibians, are usually small and easy keepers. Other than the binturong, there's almost no viverrids at all in north america, especially in AZA institutions.
I would disagree to an extent. Small rodents aren't the most popular of zoo animals, sure, but personally I have seen 134 rodent taxa in captivity and there are going to be at least as many more I've not seen. Of course, that number does only cover less than 1% of all known rodent species (which actually consist of 40% of all mammals, I think) and many of those are very rare in captivity, but it still shows that there are a good number of species being kept. I think the main problem here is that rodents will be much more popular with specialty collections and private keepers than mainstream zoos.
Viverrids I would agree with, though the issue is much less severe overseas. I have seen 14 Viverrid taxa during my travels, but only 5 of those are currently present in the United States. Of those five, three are subspecies of Binturong and the other two (Banded Civet and Cape Genet) are not AZA program species. I also only know of one other species present in North America, the Rusty-Spotted Genet, but this is also a non-AZA species.
For mammals, Herpestidae (not including meerkats) and Mustelidae (not including otters)
The problem with Herpestidae is that mongoose are seen as a potential aggressive invasive, I believe, and as such new species being brought in are generally frowned upon. To be fair, though, I'm struggling to think of more than a couple endangered mongoose species and both Common Dwarf Mongoose and Banded Mongoose are very common in captivity. I think Common Cusimanse is also present stateside, but if not at least is common in Europe along with Yellow Mongoose. One species I'd love to see brought into US zoos is the Bengal Mongoose,
Herpestes javanicus/auropunctatus palustris, which is endangered in its native habitat but introduced to Hawaii and many Caribbean islands. To me, it's a good opportunity to kick-start a brand new breeding program while also removing problem introduced predators from fragile island ecosystems.
Non-otter mustelids are another group of animals that are more common in Europe, but are still pretty present in American collections I've found. I've seen 8 species in US zoo and I know there's bound to be a couple I've not seen as well. Meanwhile, I've seen 12 species in Europe but 4 of those overlap with US zoos.
~Thylo
Typhlonectes natans may be more common, really isn't much to look at. (I've seen Sac Zoo's as well.)
