I think the biggest issue is that pro sports show themselves willing to price their core audience out of the picture.
Other than that I don’t have an answer. Other people mentioned some other issues, such as the length of games. Certainly, cultural changes impact the future popularity of sports. Lots of people no longer have lives that allow for six hours on the golf course on a Saturday, for example. On the other hand, I expect soccer to get more popular in the future, not less. I know many people under 40 who prefer it.
There’s also the competition factor. When I was a kid you had two after-school options: sports or piano lessons. Or a third option, hanging out. Now you don’t hang out, you have play dates. Kids lives are regimented and I think it cuts into the time available to become a diehard fan of a team in any sport. Entertainment options are no longer scarce as they were in the ‘50s-’70s. Before leagues expanded, getting to see a pro game in any sport was a big deal in a person’s life. My generation became diehard fans because we played sports all day, we read about them in our parent’s daily newspaper, we talked about them in the offseason, and we watched real games at Little League or Pop Warner or the local high school. When we weren’t playing baseball or football we were at home bouncing tennis balls off the wall and trying to catch them. Sports was all-consuming. Can today’s kids get that experience?
And maybe it’s not really an issue at all. So what if the NFL or MLB is less popular in fifty years? Neither of them has to last forever.