Try this one http://gtafiles.gtainside.com/downloads/ftph/1434638948_disappearing.zip (Can;t find the page of it,just the download link). Or if you want to save the care and to reappear when you restart the game this one https://www.gta5-mods.com/scripts/szabo-s-persistance-mod. Have fun.

I also have the same problem,it started when i installed a new handling for the cars,then game crashed,deleted the mods folder and reinstalled the cars that i had without the handling mod(it was a speed increase mod,for original in-game cars not add-on) and it still says the same thing " Invalid Model" Maybe it has something to do with the forced patch against the online money glitch ?