Has nothing to do with Authorize.net preventing you from moving - the credit card companies just don't want card numbers and expiration dates and so on easily accessible if your account gets compromised. I don't think you'll find any modern system that lets you take full credit card data back out. The most you'll get is the last 4 digits of the credit card number, which is something Authorize.net does allow.
You could of course layer a database of your own on top of Authorize.net and store the credit card numbers locally, but you have to be darn sure you have a million layers of security and even then it's probably illegal to do it for more than a short period of time. Not that that seems to stop a lot of companies, mind you. I've written systems for storing credit card data for a few days (encryption, data written over before deletion, etc.), storing it for longer periods would be just a matter of changing a couple variables.
