For what reason might it be that neurologists handle obstructive sleep apnea after diagnosis?

Neurology/OSA. It can be handled by doctors of many disciplines and dentists who specialize in sleep medicine. Neurologic disorders/abnormalities can contribute to sleep apnea. It's a very multidisciplinary field.
Confused. They have to have a diagnosis in order to be able to treat you, and usually it is a sleep dr or a dentist who should do a follow up with osa.
Varies. Often, specialty areas of medicine deal with the sleep apnea issues like neurologists, ENT's and respiratory doctors. It is not limited to just one specialty.

Related Questions

Why do neurologists handle obstructive sleep apnea?

Central sleep apnea. There are 3 types of sleep apnea: obstructive sleep apnea, central sleep apnea and mixed sleep apnea. Central sleep apnea is a failure of the brain to signal thru the nerves to breath. There are other sleep disorders that are also nervous system disorders. These all fall under the training of a neurologist. Read more...
Sometimes they do. Because sometimes sleep apnea (sa) is a problem with the brain not initiating the proper breathing. This is a neurological issue. On the other hand, many times sa will be handled by your pulmonologist, your ent, or even your primary care physician. Dentists can help too. Sleep studies are important in determining the correct diagnosis, and who should be on your team. Read more...
Tradition. Tradition. Neurologists first started evaluating sleep disorders. Read more...