It's hard for a film to have a large cultural impact with no memorable characters. Look at the big franchise films that have endured; The Comic Book Films, Jurassic Park, Independence Day, Back to the Future, Disney Animated Classics, Pixar Classics, Fast and Furious, Terminator, Star Wars, Indiana Jones, James Bond. They all have characters that connect, even if the stories are weak, you always come back to loving the characters.
Avatar just doesn't have any characters that resonate.
...except for one. Pandora. If you can count the world of Avatar as a character, then that is really the one character that has at least some connection to the zeitgeist. We got video games and movies attempting to capture the feel of Pandora, we got Disney creating an entire land for it at their parks. And we even had reports of people being depressed that Pandora wasn't real after they watched it the first time.
Exploring Pandora as a world is really the only possible way I can see sequel films succeeding anywhere close to the original. If they really expand on Pandora and bring it to life in new and exciting ways, then maybe they can get people excited for the franchise again.