Let nobles be able to spend these points on things, similar to how Mentors could spend their points. Everyone else would just see whatever your current maximum "score" was, but for you you'd see how many points you actually have left to spend that day/week/whatever. And they'd regenerate over time.
I dunno. I think rather than having a regenerating supply of spendable points and things to spend them on that went away (like extra hours or whatever), I'd prefer to have the points be allocatable to a set of bonuses or benefits that stuck around. ...Not sure what yet.