Doctors can indeed terminate your care. I've heard of doctors who have fired patients. They wouldn't say that the reason was that the patient was too annoying or a complainer, and that probably wouldn't be the entire reason. They do sometimes take patients to task if the patients aren't "compliant"--if they don't follow the recommendations the doctor has given.

This is usually stated somewhat like this: "If you're not going to use the treatments I've recommended, what is the point in continuing to see me?" They make it sound as if it's you who have fired them.

A good doctor (IMO) wouldn't go this route unless the recommended treatments were the only option and the patient's life depended on having those treatments. Even then, a strong case can be made for a doctor who cares enough about the patient to respect the patient's wishes and continue to deal with the issues that the patient brings in.

I can't imagine a doctor telling a patient that he/she is too annoying or a complainer though. After all, it's in the doctor's interest to keep patients, not drop them. Most doctors in my experience make an effort to follow the patient's lead, and they are usually very familiar with complainers and patients who can be annoying.