Unlike The Flintstones, who deal with a great many universal themes which are true generation after generation, Popeye doesn't. When you watch Fred and Wilma, you are getting a comedic look at the classic nuclear family, an arrangement that has existed long before the nuclear age and, barring a dystopic future, will likely continue forever. Humans just seem prone to coupling and they tend to want to raise their kids in families. The Flintstones speak to that in an entertaining way. They are also deeply "middle class," in the sense that Fred "works for a living," i.e. he does not invest or run his own business or live on welfare. They aren't social outliers either and they don't advocate crazy ideologies or religions. They are society's bedrock... pardon the pun.
Popeye is not that.
Popeye no longer resonates with modern audiences because he doesn’t project values modern audiences share. For one thing, Popeye is low class. In fact, he comes across pretty much as a drifter. He doesn't work. He doesn't raise a family. He's not capable of leadership. He doesn't contribute to society in any meaningful way. He has no sense of real responsibility. And he finds his courage in a can... sure, it's "spinach" (wink wink). Those aren't great values. To the contrary, those are the values average American look down upon.
Moreover, Popeye comes from a time when America had an inferiority complex and wanted to prove to the world that what we lacked in stale sophistication or in spiffy fascist uniforms, we made up for in being scrappy. Indeed, Popeye is a dated "ethnic" stereotype: the tough Brooklynite with little man syndrome who was inserted into every war film made in the 1940s, i.e. the unshaven thug who may or may not have a heart of gold somewhere inside, but who has no problem-solving skills and who wants to impress us with his "moxie" as he repeatedly uses violence to stand up to people we're suppose to dislike.
These characters were everywhere in the films of the 1940s/1950s. Indeed, Popeye was no different than Animal from Stalag 17 or Cagney in The Fighting 69th. Echoes of him can even be seen as late as Popeye Doyle from The French Connection in the 1970s, who responded to any insult with violence. But this isn’t someone who appeals to us anymore.
Modern action heroes use violence as a last resort after trying to fix the problem in some other way. Only when the villain refuses to change and then continues to use violence will the hero use violence himself. In effect, they fight reluctantly and when they do, they fight in self-defense and for justice. Popeye, by comparison, uses violence when he reaches the end of his patience, not because it's the only solution. That difference is key because it represents a fundamental shift in how our society views the acceptability of violence, and Popeye simply doesn’t fit in today’s society.
And the reason society has changed, I think, is because we’ve met too many people like Popeye in bars or at sports events, and we’ve seen them on Cops. These people think they are heroes and that people love how they “put bullies in their place,” but the reality is they are more often than not just belligerent a-holes. They get into fights over “points of honor” like disrespectful looks or “stolen” parking spaces or their kid’s playing time, and they engage in domestic violence when they get spinached-up. Even worse, they think “everyone” fights over those things and those who don't are somehow losers. They are a menace. Those are the values Popeye projects when translated to real life, and that’s not something people view favorably anymore.
This is why I think Popeye is vanishing from the landscape, because Americans no longer relate to or like the person his is. This is why he's different than hard-working Mickey Mouse or family-man Fred Flintstone.