My head canon is that Inuyasha is an insomniac, meaning he can’t sleep all the time or just refuses to. This started up after his mother died and he was chased by demons. To paranoid about dying as any child would Inuyasha wouldn’t sleep unless he he knew that he couldn’t keep going. Even then his sleep wasn’t good only getting a few hours at the most.
When he met Kikyo he got a bit better with sleeping, once a week he could sleep all night, but that changed after he was awakened after fifty years of sleeping. He was fine for a few months without sleeping but as the time went on he got back into the habit of over exerting himself, his human side needed sleep and he had to give into it. So he would sleep a few hours restlessly when the group was still up and keep guard at night for a few days without sleep.
His secret was found out by his group when he started to fall asleep while walking, making them worried but Inuyasha would just blow it off. Making up excuses, but they had their doubts. They finally made him something to help him sleep which it did but sometimes he just refused to drink it…not wanting to sleep and saying that he was fine.
It got worse when Kagome was gone for three years, Inuyasha became almost a zombie with bags under his eyes, but he still stayed up, his paranoia keeping him up even now.