There is a disease where you eventually stop sleeping and then die. It is called Fatal familial insomnia.

Fatal familial insomnia (FFI) is a very rare autosomal dominant inherited prion disease of the brain. It is almost always caused by a mutation to the protein PrPC, but can also develop spontaneously in patients with a non-inherited mutation variant called sporadic Fatal Insomnia (sFI). FFI has no known cure and involves 
progressively worsening insomnia, which leads to hallucinations, delirium, and confusional states like that of dementia. The average survival span for patients diagnosed with FFI after the onset of symptoms is 18 months.

The mutated protein, called PrPSc, has been found in just 40 families worldwide, affecting about 100 people; if only one parent has the gene, the offspring have a 50% chance of inheriting it and developing the disease. The first recorded victim was an Italian man, deceased in Venice in the year 1765.