The Piano API calls conversion/custom/create and conversion/log are being sent only during the first purchase. These create access to a resource for a specific period of time and subsequent access extensions are done to change the access associated with the resource. You will not need to send conversions through for renewals.
When creating the conversion, use the Piano API conversion/custom/create and set the parameter unlimited_access to true. When a user cancels their subscription or the subscription expires due to non-payment, you will need to call the Piano API /publisher/user/access/revoke to inform Piano about this.
More information is available here.
If you don’t want to grant unlimited access at the beginning, you would need to add additional calls to keep the accesses in sync. Upon each renewal of the user, you would extend the access to the resource.