oh shit! that asshole! But yeah I don't get why Ao would rewind time and not spend the whole day guarding his little sister to check what might have caused her to die?
He wouldn't be like "my sister has died so I'll just repeat today forever" . he'd repeat to day in order to try and prevent whatever it was that killed his sister, even if it meant getting doctors to perform extra tests or whatever.
then he'd see the cop come to the hospital. It's not like it would be Moe doing this.