Why do cluster headache sufferers get short of breath?

It's not common. I haven't seen shortness of breath as a common complaint among my cluster patients. It should be evaluated as a separate symptom.
Not usually. Cluster headaches doesn't usually cause shortness of breath. You may want to consult your pcp or a pulmonologist so you aren't missing something.
See below. The person with the cluster headache may be breathing faster due to the severe pain but should not be short of breath.

Related Questions

How come cluster headache sufferers get short on breath?

Unclear reason. Shortness of breath is not often listed as a symptom traditionally associated with cluster headaches. However, my patients who have cluster headaches often mention that the pain is excruciating to the point that they feel out of breath. They also tend to pace and are extremely anxious. The anxiety may contribute to the shortness of breath too. Inhaling oxygen dramatically relieves the symptoms. Read more...