To stop a subscriber's auto-renew via the API do an HTTP POST like so:
[ ~ ] $ curl -u 2dac9d3d93326f97da4845d407789da232514b48:X -X POST https://spreedly.com/api/v4/meresheep/subscribers/444/stop_auto_renew.xml
A 200 (OK) status code is returned on success. This call will stop the auto renew of the subscriber such that their recurring subscription will no longer be renewed.