When you're trying to convince someone to do something that they don't want to do, one way to persuade them is to say that it's "just this once". It means that they only have to do it one time. In the future, they won't have to do it again.
People use this phrase a lot when asking for favors from people. Like when you want to borrow money from a family member:
Can you loan me a couple hundred bucks? Please, just this once.