Dh has a low sex drive

The only available time to have sex with dh is like midnight. He works mornings and I work swing shift. But after he falls asleep all bets are off. He won't wake up to have sex. When I try to initiate sex he says I'm sleepy. So I just have to wait around for him to decide when he's ready and willing and it's very frustrating. I feel rejected when he turns me away. I've talked to him about it many times and he says he'll try to make an effort to stay up but he never does.