the Permissions for the Site Group the User is a member of. If "Can
edit their own personal account info” is set to Denied, they will
not be able to submit an order. Because adding a shipping
address is editing the Users shipping options, saving a new address
will be blocked by this setting. Changing the permission to Allowed
(which should be the case for this permission except in very rare
situations) will permit the saving of new addresses.