In truth, all any show requires to "jump the shark" is two seasons. Futurama is in its second season — and on its second network. Some critics are claiming the show has jumped the shark, but here's why this animated series is actually rallying.
The phrase "jumping the shark" got its origin from Happy Days. After five seasons, it was a show based on nostalgia for the 1950s in a world that was heading into the 1980s. The nostalgic premise mandated that the characters couldn't grow or change, and there were only so many stories writers could think up about a mildly funny family and a guy that can fix jukeboxes with a sharp smack.
This all culminated in a season premiere in which the family goes to Hollywood and The Fonz jumps over a shark on water skis. In other words, the show had declined in quality so much that it was irretrievable, and had resorted to silly gimmicks to get people to watch. (We're not even going to get into that regrettable escapade with Fonz and the time machine.)
This inevitably happens to almost all television shows, but the question is, "When?" Honestly, I thought the show might have jumped last season, when Bender quipped of a giant's face, "It's like Edward James Olmos on IMAX."
There's no reason for Bender to know of either Edward James Olmos or IMAX, and it appeared that the show was relying increasingly on contemporary references and Family Guy-style humor that made no sense, given that the whole point of Futurama is that it's set a thousand years into the unfathomable future. Why were they doing iPhone and Susan Boyle references when they had an entire universe of things to choose from? Although that season had a few really good episodes, I really thought the whole series was going irretrievably downhill.
I don't think this season has been overall as good as the pre-cancellation episodes, but I have noticed a conscious change in the show's direction, a change is the exact opposite of jumping the shark.
They've cut out many of the reference jokes and instead decided to build the show on previously unexplored relationships between characters. How do Amy and Leela interact? How do Amy and Zoidberg interact? What about the Professor's family? Instead of thinking up silly reasons about why the characters need to, say, work with the cast of a futuristic Jersey Shore, the writers are exploiting the situations that come naturally from the characters themselves. No gimmicks, just fun character-driven humor.
In fact, the Amy and Leela episode was pretty much the only episode of the entire show that I thought was outright bad. I think it exemplifies potential pitfalls with taking the character-driven approach. Amy and Leela have all kinds of differences — education, rank, parent issues — and the only thing the show focused on was, "They both fight and make up because...lady things."