When you lose a ride that you "saved" earlier by storing it in your garage(s), you should be able to pick it back up from the car impound. Keep in mind that the impound will only "store" a maximum of two cars for you, and only one of each make!
Say you lose a specific car of a certain brand, it will go to the impound assuming you stored it in your garage earlier. Then you acquire another car just like it (and didn't pick up your other car from before) and save that too. If you lose it, you'll be able to get it back from the impound as usual, but your original car (that you forgot to get) will be "overwritten" as a result (because the impound only stores one of each make of vehicle).