Glenn Kenny has a post over at Some Came Running on "A Hound For Trouble," the last Charlie Dog cartoon, and Charlie's weird combination of eagerness to please and self-destructiveness (he will do what he can to get a master, but he can't seem to resist making himself even more obnoxious than he already is).
1951 was a great year for Chuck Jones, in terms of the quality of his output; it's also a little poignant in retrospect because it marked the end of so much. The last Hubie and Bertie. The last Charlie Dog. The last solo Porky cartoon, "Wearing of the Grin" (that and McKimson's "Dog Collared," from the same year, were the last cartoons that starred Porky without some other established character to give him cover). The last Three Bears cartoon, "A Bear For Punishment." Even "Rabbit Fire" in a way is as much the end of something as it is the beginning. (Up to that point, though he'd been getting to be more and more of a loser, Daffy was still a star character. "Rabbit Fire" re-established Daffy as a foil for Bugs, the way Porky had become a foil for Daffy. It's like the cartoon is admitting that Daffy is no longer all that popular.) He still had more great cartoons to come, and even one more abortive series, Mark Anthony and Pussyfoot. But 1951 is the end of something.
Actually, a few things seemed to change in WB cartoons after 1951; for instance, that appears to be the last year when Tedd Pierce and Mike Maltese did incidental voices, as they had frequently done in the past. (Pierce is one of the chefs in "French Rarebit," and Maltese is the poor customer in "A Hound For Trouble.") At some point in the early '50s there must have been some kind of move toward purely professional voice actors to supplement Blanc, because you just don't hear the writers' voices in the cartoons after that. Also, for some reason there was a huge drop in the number of topical references in cartoons around 1952 -- there were already fewer, but for the next few years, topical jokes like the Petrillo joke (in 1951's "Hurdy Gurdy Hare") were almost gone. However, unlike writers doing voices, topical gags would make a comeback after the 3D shutdown, with Liberace and Honeymooners references becoming the norm. Anyway, the point is not that everything changed irrevocably, but that there appear to have been some subtle changes -- along with the not-so-subtle cut in timing/budgets that occurred in the middle of the 1952 cartoon lineup.
But back to the characters Jones abandoned: I guess the question remains whether any of them really could have been sustained for much longer. The Three Bears definitely could not have been; Jones specifically said that theatre exhibitors asked them not to send over any more Three Bears cartoons. All the dumped characters -- the Bears, Hubie/Bertie, and Charlie -- have certain things in common, apart from (as Michael Barrier points out) having a as much Mike Maltese in them as Jones. They're all aggressively obnoxious and, unlike Tweety, they don't try to pretend they aren't.
But more than that, all three of these series have character motivations or quirks that are unusually complicated for a cartoon series. Charlie wants someone to make him a pet. Hubie and Bertie are closer to the usual predator/prey situation, except that their motivation has less to do with survival or even heckling, and more to do with a love of playing complicated mind games. And the Bears don't really have any goals except to survive the horror of being a family. Jones and Maltese seemed to be doing this deliberately, trying to come up with character motivations that were more unusual than just "eat or be eaten." But except for Pepe Le Pew, which is really just a chase series (except he doesn't want to eat her, he wants to...), these didn't really work out. It might be that it's just hard to establish a series of short cartoons without simple, easily-processed character motivations.
Even Daffy Duck may have suffered in the early '50s precisely because his motivations -- and his characterization -- could be so different from film to film. Like Donald Duck in the comic books (as opposed to the cartoons), he was recognizable up until the early '50s as being the same guy, in broad outline, in every story, but within that framework, what he acted like and what he wanted could vary wildly. That didn't seem to get a good reception in the '50s. A character like Charlie, on the other hand, has very consistent motivations, but they're a bit convoluted by the standards of series cartoons. It's not a coincidence that he has his origin in a cartoon ("Porky's Pooch") that never produced a sequel.
(Foghorn Leghorn, I think, is the closest the studio came to a durable, successful series that doesn't have much to do with the chase format; once Henery Hawk was mostly dropped, the characters' motivations could be very different from one film to another.)