Unfortunately, I don't know of any existing VNs about relationships that don't work out. The best example I can think of is the second Memories Off game, which apparently
has an emphasis on couples breaking up.
It would be interesting to have a visual novel about relationships which are doomed to fail. If you're brave enough to write this, then there's a lot of concepts to deconstruct. (Starting with the fact that it's rare to have a high school relationship that lasts...) It would not likely be a happy story, but the main character might emerge as a wiser, more resilient person.
If you want to write about depressing topics, then consider a story where the main character has a bad habit of dating the wrong people, and the relationships don't work out.
A less bleak angle might be a story about a cursed person. This individual has been told that if they want to find true love, then they must endure __ number of rejections.
Another less bleak angle: imagine a game where in every character's route there is the distinct possibility of failure. Let's say that in this game, the first half of the story is about main character trying to pick one of the haremettes. And the second half is about whether the couple stays together. Include as much realism as you want.
This leads into another thought: what about incorporating the status of characters' relationships into gameplay? Here are there, you can find games in which
it's game over if the main character doesn't earn others' trust. Also, consider creating a game in which the main character
does not gain benefits, or gets both benefits and penalties, from trying to win the affection of more than one NPC.