its the way the game is made and limits of the xbox hardware that causes it to crash.
each model right down to every street light, car, house ect has a certain amount of polygons to load so it looks the way it does. The more simple the model (like a square box) the more you can have on screen. The more complex (like a full blown high res vehicle) the less you can have on screen. When you go beyond the max limit of polygons on screen, the game will crash.
There are a couple things you should do. One, check your vehicle dff file size. the smaller the better. 512kb would be ideal, but is some times hard to find. Try to make sure the car is no bigger than 1mb.
also, assign it to a car that doesn't spawn in traffic, because then it won't have to load as many copies at once, allowing you to have room for other cars, mods ect.
hope the somewhat answers your question