I would say they have fluctuated in popularity. After Jim passed away, the cast and the studio was sort of in a slump the same way Disney experienced after Walt died. (They went through a "What would Jim do?" kind of phase.) And it actually sort of started when Jim was still alive; in 1986, Labyrinth was released to lukewarm reviews and was a box office disappointment. Although it has since received a cult following a decade or so afterward, Jim at the time felt so distraught about the film's modest success that he kind of created a lull for himself. His latest project, The Jim Henson Hour, only lasted for nine aired episodes. For the most part, what took place between the end of Fraggle Rock in 1987 and his death in 1990 was mostly either Sesame Street or trying to negotiate agreements with Disney over his assets. But I would argue he was never the same after Labyrinth bombed at the box office.
The 1990s was sort of a mixed bag. They have released some good series out there like Bear in the Big Blue House and the short-lived Dinosaurs, and their "90s trilogy" of movies was good (Muppet Treasure Island is arguably their best from that era), while at the same time they tried rebooting The Muppet Show with Muppets Tonight which could never match to the original's standards, not to mention Frank Oz's eventual outing of the Muppets all together by the end of the decade.
I would consider the 2000s a "Dark Age" for the Muppets. Most of their film output was not as memorable as the 80s or the 90s trilogies (I've actually only seen one movie from that era), and Jerry Nelson would soon leave full-time due to health problems, losing another person that has been involved with the Muppets since the 1960s. However, they did make some contributions to the popular PBS series Between the Lions, which I liked. But overall, I think they lost their spark by the turn of the 21st century.
Now their 2010s output was kind of an improvement from the previous decade. 2011's The Muppets made an effort to introduce the Muppets to a new generation. Jason Segel was a big real-life Muppet fan and wanted the Muppets to see a renaissance in popularity. And I thought that movie was pretty good in doing that. It also left behind some pretty emotional moments in there, especially with Kermit's "Pictures in My Head" and the standing ovation scene right at the end of the movie. Muppets Most Wanted was also not very bad, even though it made me question the Muppet's competence even more that only a FEW Muppets smelled a rat with Constantine until the end of the movie! (But it may have been just a running gag, which the Muppets were known for). They have had some mishaps, such as the 2015 Muppets, which did not do as well as the film installments and only lasted one season, and not to mention Steve Whitmire's recent unceremonious departure, but I would say the Muppets have successfully ushered in a new generation of fans, thanks to the recent Disney films and the internet. I don't know what their future is going to be, but I hope they will continue to grow fans of both young and old for years to come.