Probably depends on 'where' it's being stored... A commercial facility may require current registration on vehicles so they just don't store someones 'junk'... But, if you are paying the storage fees, I don't think that would matter to them??
If you are storing on the street, I'm pretty sure you have to have it registered.
If you are storing it on your own property, you don't have to have it registered, since it's on your own property..
Good luck!
Mitch