If a patient no shows, call the person right away. If unable to reach them, let them know you will try back in about a week. Repeat a week later if needed.
If you still don't make contact, put them on automatic reminders using their preferred form of communication.
After a month or so, continue to make calls based on your knowledge of the patient without becoming obnoxious or seeming desperate. How many calls you make should be based on what you know about the patient. You can't be rote about how often you call, i.e., you know the person is out of the country for a few weeks, is ill, or whatever.