Kaylee is a mechanic on a Generational ship. The ship has several means for propulsion and has a plotted course that goes from star to star, molecular cloud to molecular cloud. It has a Bussard Ramjet and Solar Sails that get it through, most of the way. However, at this point in the story, they are in a region of space where either of these methods of propulsion aren't very useful.
They now fall back of their nuclear pulse propulsion units, ion thrusters, and other secondary propulsion units. One of these units is Kaylee's responsibility.
At this point in the story, the ship has skimmed past an asteroid clump, intending to lasso an asteroid to mine it. Unfortunately, an accident happens, and Kaylee's propulsion unit is hit by an asteroid fragment. She has to eject it, otherwise it will blow up and harm the ship.
This is bad news. It will now add a few extra generations to the ships travelling time, but the ship is not doomed.
What should this propulsion unit be, and how would the accident play out? (Actually it doesn't really have to be a propulsion unit, it just has to be anything that would have to be separated from the ship, delaying its arrival by a few generations).