Long-unseen characters made from Anything Muppets can easily be brought back for cameos or background appearances, since even if the puppets are no longer usuable, they still have the Anything Muppet bases. They don't have to build a full puppet. And the majority of non-animal characters are Anything Muppets. If characters like Aristotle, Deena and Pearl, Colambo, Dexter, Sam the Robot, and others are no longer i useable condition (and I don't know whether they are or not, though the Deena and Pearl puppets have been reused for later characters over the years), we probably won't see them in anything new again.
Though is it just me, or does it seem like furry characters last longer? There's been a number of times when Caroll Spinney claimed that the Oscar puppet being used is the same from the early 1970s, even though he's a major character, but there have been Oscar's that clearly looked different (he was a bit shaggier throughout the early 1970s, but I can't tell any difference in the Oscar puppets from 1978-2006). Or maybe it's just Caroll saying that the original eyebrows continue to be used (so do they have multiple Oscar puppets and take the eyebrows off whenever one is used? Also, it seems like the first orange Oscar had different eyebrows, with the third orange one having the eyebrows he would have). Recently it was revealed that the puppets built in the 1960s for The Musical Monsters of Turkey Hallow are still around, but had to be refurbished a little, mainly replacing the foam inside the furry bodies. And it has been revealed recently that the current Rowlf puppet has been around since the 1980s (have there been other Rowlf puppets built in recent years as well?). And in a Tough Pigs article by someone who was at the shooting locations for Letters to Santa, it was said that the same Sweetums head has been used since 2008, which surprised me at first, but in years since I've noticed that the fur looks like it's been rotting.
I've often wondered about regular characters who have been made from Anything Muppets. Somebody who worked for either Henson or Sesame Workshop in the past noted at Muppet Wiki that when Anything Muppet characters start to get used more, they build a more permanent version of that character. I wonder how many characters are not done that way (I could see them not doing that for Little Jerry and the Monotones, or the Busby Twins, or Leslie Mostly). Surely they made permanent versions of The Count at least, and it seems they have for Guy Smiley. But in one of the interviews with Jim Henson on the Sesame Street: 40 Years of Sunny Days DVD, he refers to The Count as an Anything Muppet as if they were still only making The Count in the Anything Muppet way (meaning they only decorate the blank Anything Muppet and dress him up when the character is needed).