I don't think it is sleepless because it is much used for sleepless nights not for people, but I found an incident in Coca where it was used to describe a man. Anyway, if you have a sleepless night it means, I think, that you want to sleep but you cannot because you have a medical condition whatever level it is, but not because you have a lot of work you want to finish.
If there isn't any, then I would like to know if there is a word that describe someone who does not sleep a lot at night because that's his nature or they love night life.
It is an old house, painted white and well kept, standing behind a low stone wall tufted with moss, and it dates back to 1790. There are many rooms for a sleepless man to walk through. I knew that if I were a better person, I would have stayed up with him, the way I used to do each year. But I was tired, and longed for sleep the way I used to long for the press of our two bodies. And besides, I didn't want to go through this yet again. The wife : a novel by Wolitzer, Meg.
Note: if you think the title of the post is not quite right fix it please.