It will be fixed automatically. Don't listen to the rumours that are going around stating that the engine rebuild/chassis maintenance option have anything to do with damaging your car. They don't.
This makes me feel better, do you have a source? I've been worried about driving my pricey cars around because I certainly can't afford all the rebuilds. Perhaps the most unfinished thing in this game are the instructions.
You can test it yourself. Buy a new car, drive it without crashing and after a few miles, even before the engine is completely broken in, it will enable you to rebuild both the chassis and the engine.
Both rebuilds come with a fixed price depending on the car's price, by the way.
I also found cars seem to get better after a couple of races after being new, the engine seems to go faster and like you said "Broken in".