RadioLab recently covered an interesting database on quicksand scenes in movies. This database was compiled for that most human of reasons: sexual kink. But like all databases compiled for sex, we can analyze the data for non-sexual reasons, if we have a reason to. Or if someone just wants to and works for Slate; in fact, this analysis happened in 2010 by Dan Engber, who noted that there was a rise in cinematic quicksand until the 1960s and then a drop-off. He also noted that metaphoric quicksand had a peak in the 1960s too, with Vietnam being "quicksand" the US was stuck in, to worries about lunar quicksand faced by the Apollo. So the 1960s were a particularly anxious time for America, quicksandily-speaking.
Which seems like a good observation until he undermines his own thesis by noting how quicksand has had a long, pre-cinematic life during the Age of Discovery. He even notes (without graphs, unfortunately) that quicksand dotted the frontier of Manifest Destiny literature. So, from there, we move on to the theory that quicksand symbolizes something about unknown areas: about the way that explorers might get swallowed up by the wilderness they sought to explore. When you push the limits of the known world, sometimes the unknown world pushes back--by pulling you further in. That's a fun idea, a sort of exploration-judo, where the unknown uses our own pushing against us.
So really, the 1960s weren't "peak quicksand"; only that our worry about engulfment and quagmire shifted from African jungle to Vietnamese jungle and lunar wilderness; and that we had a particular visual medium that was very friendly to the slow sinking action of quicksand. (Quicksand in a movie--exciting and incremental and inexorable. Quicksand in a comic book--what is that, dirty water?)
But then we're back to the first question: why did we have so many adventurers in quicksand in the 1960s and why did it drop off? And, additionally, where did it go? Engber talks about the drop in sandboxes as part of our loss of the quicksand trope, but it seems to me that we need to think about generations as the only way to describe how a trope falls out of favor in a particular medium.
That is, in the same way that a serious use of a trope will precede its parody, so a trope that thrilled us as kids may well get more play when we're the ones making the movies; and so the trope that we're invested in may well seem dated to our kids. (The loss of sandboxes in NYC will only have some effect on what's being made out in LA.) We also have to take into account the way different media absorb and deform certain tropes.
In other words, the reason why quicksand had a bump in the 1960s probably has more to do with the adventure serials of the '30s and '40s. It's easy to fit a quicksand scene into an episodic narrative. "Did you see Episode 12, where they get caught in quicksand? It was amazing!" But try to put that quicksand into a film and it fades a little in importance: what's more frightening, the quicksand that couldn't move to get the hero at the 30-minute mark; or the cannibal tribe that chased him at the 32-minute mark?
So people who were entranced by serial quicksand in the '30s and '40s start putting it into movies in the '60s--it's still good for a cheap thrill. But the kids in the '60s aren't so worried about quicksand and so it filters down into the cartoons and tv of the 1980s, either as momentary problem or as comic relief.
And this is also why, I would guess, quicksand hasn't made a huge comeback in video games as a serious threat. There are moments of quicksand in some Mario games and others, but seriously: in a medium that prizes interactivity, how much use will creators get out of a trope that works to take agency away from the character?