Her request was quite weird... no... he knew that she had been acting weird even before he stayed in the camp. She said or did something which she had never done before.
The fact had always made the Crown Prince uneasy but... what could he possibly do? It's clear that she was unwilling to say it to him. He couldn't ask or pressure her and instead, he decided to make her feel better.
He doesn't have much choice.
"That will be hard," he muttered.
Why did she talk as if she was sure that something would happen to her while he was away? He thought of many possibilities but... her real reason for saying this had never once crossed his mind!
It's that hard to guess.
Iria Alewine remembered him saying that he didn't make an empty promise. So, it would be useless to pressure him to give her his word.