It was about time we had Donnie Darko on the Black Box. It is a very interesting case - not so much for a complicated time-travel loop or paradox, but rather for the way it tries to fit a simple situation into a coherent description of Time-travel that combines real science with a fictional framework, described in the book "The Philosophy of Time Travel" that appears in the film (in particular detail in the Director's Cut).
The information given in the Director's Cut and official websites does not give a unique and exhaustive explanation of the events. In fact there are various interpretations out there that are consistent with the film. I would like to point out and comment two.
First, as explained in a dedicated UK website, the situation is explained as a disruption in the fabric of space time that happens by which the primary timeline is put on hold while an alternative timeline (a "tangent universe") is generated that will last few weeks. In the process of "copying" the primary timeline, a glitch results in the jet engine being copied twice. Having the same object twice in the same timeline could cause that the tangent universe closes catastrophically when the time comes a few weeks later, so someone (Donnie) needs to be guided (by the Bunny and others) to get the second engine out of that universe -- through a time portal to the primary universe, where it lands in the house eventually killing him. This interpretation is quite sophisticated and thoroughly designed, but for my taste in invokes too many "ad hoc" assumptions that are not hinted at in the movie: the glitch, the need to remove duplicate objects, and the fact that duplicate objects are not a problem in the primary universe, just in temporary tangent universes.
I therefore like this other one better, as it makes fewer such assumptions, and the ones that it makes are supported by some subtle hints in the film: a disruption in the fabric of space and time makes the falling jet engine travel through time to the past, where it lands on the Darko's home. What we see in the film is just one of many loops in which Donnie has tried to avoid the accident in the first place. So far he has not succeeded, but this time he manages to get the engine through the time portal again (it would not normally happen in the tangent universe, as it would be too much of a coincidence for this anomalous event to happen again in exactly the same moment and manner): it kills him, but by having an engine in the original timeline that is a duplicate of the engine of the plane in which his mother and sister will be flying 28 days later, leads the aviation investigators to check the original engine on the plane and avoid its malfunction, and the accident. Donnie has sacrificed himself to save his mother and sister.
In terms of time travel, once the disruption has happened without explanation, it is clear that the future is not set in stone, and if it has changed for the worse (jet accident) then it could at least changed again in order to mitigate the devastating effects. With the help of time travel, Donnie and his helpers, try to break the time loop that has been generated, not by avoiding that the falling jet engine travels to the past, but by making it travel to the past again. The originally generated time loop is closed and self consistent, but by breaking it, a linear timeline is restored (jet travels through time, but no accident occurs later), which is different from the original one (accident, but no jet traveling though time), but at least better that the one with the embedded time-loop (accident and jet travelling through time). Don't these three options remind you of a Moebius strip?
More on interpretations of Donnie Darko in.