You can unsubscribe from someone's prayer requests by clicking on the Unsubscribe link at the bottom of an email notification:

Alternatively, you can log into Prayvine and unsubscribe by clicking on the settings button in your conversation thread with prayer request sender. You will stop receiving notification emails, but will still be able to view the sender's prayer requests by logging into Prayvine. Alternatively, you can leave the prayer team; you will stop receiving notification emails and be unable to see the sender's prayer requests on Prayvine.