Blue Valentine. The realness of their relationship just made the inevitable split all the more heartbreaking, and that final scene of their daughter trying to chase Ryan Gosling and call him back was an absolute killer.
re:Blue Jasmine.
Not sure Jasmine's character (Cate Blanchett) would qualify as "love story". She is what Sera (Elisabeth Shue) was in "Leaving Las Vegas".
What I'm looking if more along the lines of, for example, in "True Romance", if Christain Slater were to die, I would've qualified as heartbreaking love story. Or, Bruce Willis in "Sixth Sense" is another one that comes to mind. "Days of wine and Roses" has a dark ending but not necessarily a "sad love story". "Gatsby" is another example.
Not quite sure what you're looking for but I'll spitball some stuff:
A Walk To Remember
Fault In Our Stars
Blue Is The Warmest Color
Remember Me (Which was titled "Memoirs" when it was a script and it has one of the best twist endings ever -- though they took the backstory that goes with the twist out of the movie and it's not near as effective. I bawled my eyes out reading the script!)
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