There's no such thing as heart-losing here. In Hard mode you actually need to use heart containers on girls to be able to increase relations with them, that is to get new red hearts. If you not add this containers in time, at some point you will not be able to do so before the scene that adds a heart plays out. And since you didn't add a container, you will not get this heart and will have to buy it in Bonus area for 1 coin. I myself lost 2 coins that way, and I was lazy enough to replay some parts of the game. So now I'm 2 coins short to buy all available outfits, although that's not really an issue.
Thus, a rule of thumb is like
@Trapezio said: use "Heart up" as soon, as one of the girls gets a new red heart and doesn't have any free heart containers. If you find all heart containers up to this point, all girls will have one free heart container and you'll have a spare one in inventory also.