The NFL itself will continue to flourish. What has really changed is the nature of fanship.
I believe that you are seeing fans that are more loyal to particular players than the teams they play for.
I think this is a combination of several factors. First, there is free agency. Before the mid 90's most players, especially the top tier ones, played for a single team in their career. There was no conflict of interest when rooting for a particular player on a team because he was going to remain with that team about 90% of the time.
Yes, there were trades and some players were able to get picked up by another team after being waived. However, in most cases, fans were able to enjoy teh full careers of their favorite players on a team. We experienced every phase of their careers, the hopeful rookies with all their potential, their emerging contributions to the success of their teams, their prime productive seasons and their years as an experienced older veteran.
Nowadays, the player you love on your team eventually becomes the player you root against on a different team. this creates a conflict of interest among the fans. Some have strongly identified with a particular player and it is difficult to make the choice for many of the newer fans. At the very least, it has diluted the intensity of loyalty to teams. It has made rivalries less relevant.
Another reason is the popularity of fantasy leagues. Who will you be more loyal to, the players on a particular team or the players that you, yourself, created and is using to compete against other teams? If someone is a Cowboys fan but they have an opponent player that must score in order for them to win their fantasy league game (and win money), where does their loyalty truly lie?
An additional reason is our ability to access so much information about the players. there are no longer many secrets and we are privy to just about every facet of their daily lives. As such, they are no longer "bigger than life". They are involved in so many other enterprises, creating their "brand" that the players seem more like mercenaries than loyal members of the team you root for. Loyalty given is not always equal to loyalty received and I think fans are more aware of this.
The rule changes and certain innovations, combined with contract issues and the salary cap has also frustrated many fans who have reacted to placing less emphasis on being a sports team fan. Older fans may feel as though they don't even recognize the game any more.
Of course, I am referring to "average" fans. That's not us. We're crazy. We'll spend an hour or two several times a week discussing every nuance of the Cowboys. However, I feel as though we are a dying breed.
It's not the NFL that is declining in popularity, it is the overall degree of intensity that fans feel for their teams that is declining.