Why can't I store the Attrazione in Saints Row the Third?

If you customize it in a garage it will automatically be stored in your garage, it might also be that you have 50 vehicles and cannot store anymore

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.