I don't think there is a "third film" curse, for any movie. I think by the time a third picture rolls around audiences are expecting more (in this case, the third being better than the previous films) and the filmmakers always look to go in a different direction while making contrived connections to previous installments.
All third movies rely on the same cliches for the most part. They all usually go back to the beginning, they usually rely heavily on flashbacks and they create unnecessary questions and dilemmas that rub people the wrong way. You can see where they're going from miles away. When it gets to the "third one" they tread a fine line of familiarity with the audience (people want to see a continuation of what they loved) but with this new, unique weirdness as well. By the third film (during or after release), I think people just get sick of it, the fans, audiences, and the people that were involved in making it. It's a "been there, done that" situation and what once made it great has gotten old.
In my opinion, unless it's something like Lord of the Rings (three films based on a book, filmed and released simultaneously), filmmakers should just stop after their second film, successes or not.
Looking at the three different Batman pictures (Nolan, Burton, Schumacher), each one of their interpretations starts to get bogged down with the director's vision as each film progresses. Their styles and approaches become more apparent. With Batman Returns, you can see it's much more "Burtonesque". While I love Batman Returns, I can't imagine what a third Burton film would have been. It probably would have been an even farther departure from the first. Batman and Robin is like Batman Forever times 100. The neon is pumped up to the max, the obnoxious qualities like buttshots and corny cheese is featured in every scene, another hero and villain is added etc. etc. With Nolan, it's TDKR. Everything is just heightened and bloated versions of Begins and Dark Knight. It's like the exact opposite feel of what Schumacher did but similar in that the sequel is just a "bigger" version of what they had done previously. The characters can't just be themselves and act naturally, they always have to be some theme and "something more" (even established characters like Batman and Gordon with two stories under their belts). The story has to be larger and the stakes have to be higher despite it being as high as it should have gone in the second film and the characters suffer for it.
It just gets excessive and I think the filmmakers, storytellers, whatever start to lose sight of what makes the character their adapting great in the first place.
