The longest Izzy stayed up on Earth was 2 and a half days. And there had been times when she's operated on very little sleep. Most of the time it had to do with friends or schoolwork. With the occasional tv or movie marathon. And as one would expect it deeply impacted her ability to do certain things. But especially excuses.
She once told her wrestling coach that she couldn't do anything that day because Thor ate a wire in her arm. She had completely forgotten that she had shown her arm to be fully functional throughout the whole day.
Out here things are not much different. She can stay up longer because of the regenerative abilities of the gedutu. But she still can't avoid sleep entirely. She's had elaborate excuses for why she can still go on missions. But when she's really tired all she can muster is "I'm fine." If she hasn't already fended things off with a joke.
This excuse will do for now though.