Both the fiance and I have had trouble storing the Attrazione car in our garages in Saints Row the Third. We've been able to find them, drive them, and take them into our garages; but once they're in there, even if we press "Y" (Xbox 360, standard control setup) to store it, it doesn't store--it will remain in the same location in which it was parked rather than disappearing, and no message displays saying that it has been stored. When looking at the stored car list, its name does not show. Additionally, after looking at the stored car list, the Attrazione disappears (and is still not stored in the garage). We have had this problem on each of our profiles, and we play on the same Xbox 360 console. This has occurred on different days after various turnings-on and -off of the console. Does anyone know why we are unable to store the Attrazione in our garages?
I'd be interested in knowing where you're trying to store the car. I'm playing the Steam version of the game and whenever I try to store a car in the Burns Reactor crib (North-East of Kinzie's crib) it won't let me. It doesn't matter which car, and it doesn't matter which save I'm trying from. For me, it's just a glitch I know about so if I want the car, I go somewhere else to store it. I have had several Attraziones in my garage over time without difficulty although I have to say that I prefer the Neuron as it has far better handling. :)
There is a limit to the number of cars you can store as has been mentioned, but before deleting cars, just try saving it in other cribs, at a Rim Jobs, etc. Also, if you DO delete cars, remember that reward cars don't count to your total so you have to delete cars you've captured yourself to clear a slot.
Good luck with it.