Most decent processors have processes in place for the transfer of CC numbers. I was involved with this process at a decent-sized magazine, it involved armed security, an encrypted hard drive in a locked container and millions of dollars of insurance. It's not an easy process, but is possible.

Sounds ... expensive.

Some will let you export the data, but it's a hassle. They burn it to a DVD and ship it to you and you have to sign tons of stuff freeing them of any liability.

Otherwise you just ask customers to re-authenticate. Often you have a few months headway for a switch like that.

Said processors allow you to export credit card data to another processor without having to store it yourself.