Honestly, I don't see why the classic Muppet style doesn't appeal to a younger audience. Maybe it's because I grew up with them, and maybe it's because I was exposed to a lot of older entertainment growing up (like Laurel and Hardy and the classic musicals). Those things just seem like they would never lose their popularity. I think the Muppets could stick to their original style, and they would be relevant and would attract the crowds. Perhaps?
One example I could think of is how fantasy/adventure movies sort of phased out a very long time ago (back in the fifties?) , but now they're starting to make a comeback. I don't think they ever lost their appeal, it's just that people were caught up in more realistic films. If they had just continued making them, I think there still would have been an audience for them. The Muppets will always have an audience just doing what they do best, I think.
Remember, too, the Muppets were sort of considered rebelious humor when they were first introduced. Kids today are obsessed with being rebelious, so that's even more reason why they should like the Muppets without the Muppets having to change for them!