Mr. Oates always sleeps restlessly, snorting and gasping throughout the night. It is most likely that Mr. Oates suffers from:

Mr Oates suffers from sleep apnea

Explanation:

sleep apnea is a breathing disorder, characterized by a repeated cessation and starting of breathing, which might last for a few seconds to a few minutes during sleep. This disorder is characterized by loud snoring and choking or snorting sound which is heard when breathing resumes after the brief cessation of breathing. This leads to sleeplessness and tiredness on the subject. There are two types of sleep apnea:

Obstructive Sleep Apnea (OSA): here, there is blockage of free airflow

Central Sleep Apnea (CSA): there is an unconscious cessation of breathing

there may be a combination of both.

the answer to your question is (pancreas).