Please take a look at this questions and its answers:
http://gaming.stackexchange.com/questions/131250/how-does-the-garage-system-work-in-gta-v

If you customize a standard car, you have to at least once save it in a garage (the big ones, not the one next to your save house). If it gets destroyed during a mission or while cruising through the city, it will then re-appear in the garage.

But if it is stolen or abandoned (or replaced by another vehicle during a mission cut-scene), it gets impounded. You have the chance to get it back for a fine, but there is only one slot for impounded vehicles, so with the next car you loose, your first one will be lost forever.

I'm not entirely sure where to get the impounded vehicle. (Probably the parking lot next to the police station where the tow truck missions start.)
I'm also not 100% sure if the impound-ability gets reset when repossessing the car, when it's saved in the garage again or even never at all.

Also there are reportedly some glitches happening. So your car may as well vanish from your garage, may be replaced by another car in the garage, may never be impounded or not saved after repossessing it. Good luck!