There isn't a easy way built in. You could go about it in various ways. A couple ways (and not limited to) are:
* Have a copy of the messages to a mailing list sent to an account. Create a utility using SOAP to connect to the account to pull out attachments from emails in that account.
* Have a copy of the messages to a mailing list sent to an account. Use
WebDAV to access the /attachments folder and copy them off.
I'm sure there are many other ways to automatically grab attachments and save them off.