At this point, the Simpsons has been on the air for 22 years. There are grown people with jobs and families who have not lived in a world where the Simpsons wasn't on the air. There have been people complaining that the show is past its prime for an entire decade now. Much like the Queen, the show is now something that seems to have always been there, an enduring monument.
But the Queen is 85, and suddenly it appears the Simpsons might not be long for this world either. The problem doesn't have anything to do with it being an elderly lady in the public eye - that would be silly, it's an animated TV show - but more to do with money. While the show is still profitable, with merchandising and advertising allowing Fox, the network behind it, the ability to make a grain silo full of money to swim in like Scrooge McDuck, it hasn't been all sunshine and rainbows. The voice cast, which has been an integral part of the show's success, wants in on that merchandising, and Fox thinks they are getting more than enough money as it is.
It could be a negotiating tactic, but the threat doesn't really seem that empty. Fox has other successful animated series, or they could just start re-airing them from the beginning, as by now everyone has probably forgotten a TV show that aired 22 years ago. While the show has made them a great deal of money, selling it into syndication could be similarly profitable, and would make a large chunk of change without having to pay people a considerable amount of money to make new content - that voice cast makes $8 million a year each as is.
Even if the series is cancelled, the various spin-off benefits aren't going away. While I'm certain someone would dispute it if I declared it this generation's Peanuts, it would be that comic strip's equivalent in posthumous activity. The strip was cancelled in 2000, after the death of creator Charles Schulz. Yet, eleven years on, the characters are still on a large amount of merchandise, and the strip runs continuously in reruns in newspapers and online. It is even getting the archival treatment, with complete volumes being treated like important cultural artifacts in their presentation. It might not have new installments, but it's not going anywhere.
The same deal will happen with the Simpsons, whether the series is cancelled due to this contract dispute or it continues on for another 22 years. It is a series that has become such a cultural force that there is no way to get rid of it, and the merchandising is so prevalent that the characters are inescapable. With syndication, anyone with a basic cable package will find it's entirely possible to watch the series for an entire day without seeing the same episode twice. It doesn't need to have new material, it has enough to sustain a merchandising empire all on its own.
There are plenty of people who view the show as past its prime and would welcome the production of new material ending. Even I haven't watched a new episode in years, since at the time I thought it had a major quality drop. But, even if the new material ceases, the show will never actually go away. The Queen will some day die, but she'll still be on our old coins. Similarly, while the series might be cancelled, the Simpsons will exist until the end of time, whether we want it to or not.