The book "why we sleep" as I understand suggests the increase in probability of dementia if you don't sleep enough i.e., lack of sleep leads to brain damage that is not fixed by sleeping longer later.

It's more about the quality of sleep as perfect sleep seems to be able to reverse Alzheimer's in mice . Without some kind of chemical intervention there's no way a complex system like the brain will fix itself, the bad sleep further deteriorates the brain's ability to get good sleep and each day the problem gets exponentially worse. https://www.ncbi.nlm.nih.gov/m/pubmed/25457559/

Also possible long-term health consequences.