Sleep Cycle has an optional Premium subscription.
Once you're a subscriber, you can manage your subscription from iTunes or on your iOS unit after purchasing it, and you'll also be able to cancel the auto-renewing subscription from there.
Deleting the app does not cancel the subscription. You can, however, cancel a subscription even after you've deleted the app.
The subscription will auto-renew 24 hours before the subscription period ends, with the same kind of subscription you already bought, to the same price.
For more information please refer to these articles.