I think popularity is waning for the .44, particularly the .44 Remington Magnum.
People who want a powerful, but pleasant to shoot, more easily controlled big-bore are finding the .45 Colt superior.
For those who need, or just want, absolute power there are several calibers to top the .44. .454 Casull, .460 S&W, .500 S&W, etc.; none of which existed in 1955.
The .44 magnum appealed at its inception to essentially two categories of people: Those who wanted it because it was, after all, "the most powerful handgun in the world and will blow your head clean off" [raising my hand; "guilty your honor] and those who hunt with a handgun or need it for protection against dangerous animals. When I was stationed in Alaska in the mid 70s very few people could scrape up enough money to buy one even if one could be found for sale.
Today it's in no man's land. It offers nothing over the .357 for defense against two legged vermin and for wow factor and pure power there are better choices.
Prior to the release of Dirty Harry, the .44 Magnum was dead. S&W literally stopped making 'em when Dirty Harry was being made and S&W had enough inventory on hand since they weren't fast movers. The guns they made were just sitting on their shelves, slowly being doled out to a few orders here and there.
The moment Dirty Harry hit the silver screen, it was a hit and orders for the .44 Magnum jumped through the roof. Then, for a few years afterwards, you'd find a used .44 Magnum with a 3/4 full box of ammo for sale. Why? Because the novice shooter purchased it, usually someone who never owned a gun a day in their lives, and they discovered the recoil was stout.
Well, that didn't matter..44 Magnums were still gaining popularity. Ruger started to make one as did Colt, Taurus, and Astra Then, the 1990s and early 2000s happened and revolvers plummeted in popularity.
But the mighty .44 Magnum kept right on trucking. They never lost popularity.
And the 2010s happened and you had increased popularity. To where now, the .44 Magnum is king of the magnums.
For the North American continent, the .44 Magnum can handle everything.
Sure, is 10mm gaining ground due to a resurgence in popularity? Yup. And 10mm is here to stay. But it can't do what .44 Magnum does.
And .45 Colt can't do what .44 Magnum does since the majority of the guns chambered for it aren't older large framed Rugers. The heavy duty Ruger only loads were meant for the large frame Vaqueros and Blackhawks. Not a S&W Model 25 and a Uberti or Colt 1873. Heck, even the current production Vaqueros and Blackhawks can't take those stout Ruger only loads.
And I'm a .45 Colt fan. But I know that .44 Magnum is the better of the two cartridges.