There are two failures of storytelling that can cause me to lose my suspension of disbelief:
Violating Established Rules
In Act I through the first half of Act II, the story should establish the rules by which this fantasy or scifi world operates. This is usually told from the perspective of the protagonist, who is thrown into this new reality along with the audience. A mentor character will often be introduced to teach the rules.
In the latter part of the story, no new rules should be introduced nor should the established rules be violated. The introduction of new rules at the last minute is an example of deus ex machina, which is not viewed as good storytelling. By establishing the rules early and sticking to them, it gives the audience a framework for what to expect for the rest of the story.
NOTE: You might be able to get away
with breaking/bending the rules if you
provide adequate foreshadowing that
the original rules might be false
and/or have loopholes.
Positive Example: The Matrix (part I)
Once Neo leaves the Matrix, Morpheus teaches him how the Matrix works. He then provides a bit of foreshadowing: most people can't break the rules, but Morpheus believes Neo can.
NOTE: These rules were broken in the
sequels without adequate explanation
of why. Totally ruined it for me.
Negative Example: Superman II
Lois learns that Clark Kent is Superman during the course of the movie. At the end, he kisses her and she completely forgets this one fact (and the events that occurred during the course of the movie, I suppose). Truly sloppy writing. The writers set up an extremely dramatic situation--the secret of Superman's identity is out. And instead of allowing this revelation to drive the story, they make it completely go away without any consequences to any of the characters involved.
It's just like a reset button on a video game: good for games, bad for storytelling.
Poorly Written Characters
I can suspend my disbelief to cover some crazy violations of physical reality as long as the characters are compelling. When the audience is caught up in the character's emotional journey, the details just aren't as important.
Positive Example: Spiderman II
In this movie, Peter Parker loses his superpowers in a way that is never fully explained within the context of the rules of the "Spiderman reality." It turns out that the disappearing powers are a physical manifestation of the character's internal struggle--and it works! We don't need to know more than what is given. If the writing and acting behind this character had not been as believable, this lack of explanation would have kicked me out of the experience.
Negative Example: Nearly every Michael Bay movie
Simplistic one-dimensional characters who are parodies of themselves. They make choices that are not believable within the context of human nature.
Specifically, the movie Armageddon. By the midpoint, I was noticing and getting highly annoyed by violations of physics. I had already been kicked far enough out of the story by that point to start nit-picking the details. I didn't care about the characters anymore.