Insomnolence

Insomnolence is sleeplessness, and, in this instance, we use it to refer specifically to cases of persons who claim to never sleep, either due to traumatic injury or other causes.

Al Herpin (1862-1947)
(born 1862?; died January 3, 1947) was an American known as the "Man Who Never Slept"

William Warner

 * "William Warner, who lives near Great Barrington, Mass., says, and his statement has never been disproven, that he has not slept for 30 years. He is 60 years of age and physicians are baffled by his case. His health is seemingly perfect and he extends an invitation to any physician to come and study him, spending as long as he likes. He goes to bed for the purpose of resting but never sleeps and reads until daylight, when he arises and goes about his work as refreshed as if he had a full night's sleep. He has never tasted tobacco or liquor in his life, but is a great tea drinker. He is a bachelor and does all his own household work."

John E. Healy (d. 1951)

 * "BEVERLY, Mass (UP) - John E Healey, 94, who claimed he had not slept for 30 years, died Monday. Healey claimed he rested by sitting in a chair four hours night..."

Paul Kern (d. 1955)
(? - 1955) was a Hungarian insomniac. As a soldier serving in the First World War, Kern had been shot in the head by a Russian soldier in 1915, damaging his frontal lobe and leaving him unable to sleep.

Pledmontese Mario Solfo

 * "Eighty-four-year-old Pledmontese Mario Solfo is believed to hold the world's record for wakefulness as he has not slept for 30 years, says a Turin report. Sleeping tablets have no effect on him. To help him get through the night he has a large meal at about one in the morning and then does crossword puzzles until about 7."

Mabiano Geonson

 * "Manila, Fri. - A father of nine in Mindanao, southern Philippines, has not slept for 30 years. He says he would give away everything he has for a good night's rest. Mabianao Geonson, 40, claims that he has not slept soundly since he was six. Only four years ago, he says, could he take naps of up to 30 minutes each day. He complains of being perpetually tired and wornout but looks healthy and robust. Geonson has three physician to back his claim of a life without sleep. [...] Dr. Ramon Abragan says he has given Geonson the strongest sedatives but has been unable to induce sleep. Another tried morphine, that also failed."

Fyodor Nesterchuk

 * http://en.ria.ru/rian/index.cfm?prd_id=160&msg_id=5309602&startrow=1&date=2005-01-14&do_alert=0 (link dead) "KIEV, January 14 (RIA Novosti) - Fyodor Nesterchuk, 63, of the town of Kamen-Kashirsky, Ukraine's Volynsky region, has not been asleep for the past 20 years. No soporific can do the job and no doctor has managed to put him to sleep even for half an hour, reports the Ukrainian private ICTV channel."

Thai Ngoc
(born 1942), Vietnamese insomniac. According to Vietnamese news organization Thanh Nien, he is best known for his claim of being awake for 33 years.

Li Zhanying (河南婦)

 * https://www.bastillepost.com/hongkong/article/9120842-%E6%B2%B3%E5%8D%97%E5%A9%A6%E8%87%AA%E7%A8%B140%E5%B9%B4%E5%BE%9E%E6%9C%AA%E7%9D%A1%E8%A6%BA%E5%8D%BB%E4%B8%8D%E6%84%9F%E5%88%B0%E7%B4%AF-%E5%B0%88%E5%AE%B6%E6%8F%AD%E9%A9%9A%E4%BA%BA%E7%9C%9F "According to reports, Li Zhanying, who lives in a rural village in Zhongmou County, Henan Province, said that she has never really slept since she was 5 or 6 years old. This 'non-sleeping habit' has been maintained for 40 years[...] Experts interpret this phenomenon as 'sleep when awake.' Just like sleepwalking, Li Zhanying's body parts of the nerves and organs are still active during sleep."

In Fiction

 * Michael Traile, "the Man Who Never Slept" (or "Man Who Never Sleeps"), a spy who suffered chronic insomnolence from childhood after an operation to repair a skull fracture caused irreparable brain damage, who was the adversary of Dr. Yen Sin in the magazine of the same name in stories written by Donald E. Keyhoe.