It's practically meaningless to predict any pop culture phenomena past a few years. There's just too much change in society, people's interests, and in the way art is done to make such predictions meaningful. Big watershed games change everything: Doom got eclipsed by the later generations of first person shooters culminating in the watershed of Call of Duty; The Dark Knight defined action movies to a massive degree but Avengers brought blockbusters back to a more idealistic and Star Wars-type tone; and whatever one thinks of Twilight, it certainly influenced a generation of horror, romance and supernatural storytelling.
That having been said, a franchise as old as Call of Duty doesn't disappear. It may go into hiatus, but it will eventually be revived. As any Sonic fan can tell you, a franchise can survive for multiple console generations on the strength of a few beloved installments, even if the most beloved chapters of Sonic themselves actually may not hold up that well.
The big warning sign for the franchise is the juxtaposition between the response to Battlefield One and Call of Duty: Infinite Warfare. It can be difficult to gauge fan response to anything, and even here we have to bear in mind that a lot of people are likely to ultimately buy a game like CoD having not heard at all about the controversy. Still, this is the kind of era-defining moment: it should be telling Activision very loudly that their franchise is publicly perceived as stagnant, uncreative and uninteresting.
Worse, that kind of casual name-recognition buy is not a good thing for a franchise. Last night, I downloaded Pokemon Go. I haven't been into the Pokemon franchise to any real degree since the 1990s: the last time I beat a Pokemon game was probably on an emulator in the 2000s. I'm not at all a Pokefan, though I do appreciate a lot of the series' merits from a distance. But Pokemon Go is such a phenomenon that it excited me. There comes a point where something is just so big that participating in it helps you be part of the zeitgeist.
That's what game publishers want, and you need occasional games that are that big to keep a franchise's staying power. History is littered with franchises that were once some of the most iconic brands in gaming that are struggling or practically dead: Konami's lineup alone is practically a graveyard of some of the most influential and beloved properties in the whole history of gaming, and Mighty No. 9's abject failure to build off of the success of Mega Man 8 and 9 means that it will be very difficult for us to get a new Mega Man (which was, in the interest of full disclosure, my jam and a huge part of my childhood). Think about the last time there was a great TMNT game.
Unless Call of Duty does something as big as Infinity Ward originally did to the franchise, they're in real trouble. And they'll already be working from behind: Even if the game is a commercial success and redeems itself critically, people are already asking before this title is even out, "Will you be doing anything different with the next installment to justify me giving you my hard-earned money"?
I predicted 6-9 years as a result of this. CoD is just too big for it to run out anytime before then: it'll pump out at least a few more games no matter what. Beyond that, there are two scenarios: One where Activision goes back to the drawing board and finds something fresh to excite players; and one where Activision doesn't and Call of Duty becomes an also-ran.
Given Activision's history of running immensely popular properties into the ground (remember Guitar Hero and Tony Hawk?), I'm not holding my breath.