I've thought for some time that it's really impossible to have a genuine love story set today. As Allan Bloom says at one point in his book, "we keep going back to the bottom of the barrel and coming up empty." Romantic love between man and woman is the signature invention of Christian civilization in the middle ages (partly as a reaction to Christianity, and an overcoming of it), and replaced religious passion as the foundation of the arts. Without it both the arts and actually life--if by this one understands something beyond mere life--have become sterile and boring. Much of modern anomie is to be understood as the drying up of this source of vitality. There were some genuine attempts to replace it with something new in the 1920's but both German nihilism and existentialism are crisis-mode attitudes that are too dependent on historical events and in the end too dour to serve as the foundation of arts and of life. Without longing and fanatical belief in sexual passion (romantic love) there's really little to live for. And I think it's not possible to have genuine love stories told in movies or books.
I can think only of a couple of examples of movies, and both are Asian. I think this is because there are still some social obstacles to strong individual sexual passion in Asian culture. Love stories depend on demonstrating the primal superiority and power of sexual love over all merely human conventions, tribal laws, etc., all obstacles, even to the point where lovers are willing to sacrifice their lives; Romeo and Juliet is the blueprint, but even when it doesn't come to death, that has to be a possibility, and the principle of obstacle is the same. Well one big problem is there aren't any obstacles to conquer and partly as result, partly as cause, Western people pretend to take sex casually. Of course they can't take it casually which is why this leads to sexual dysfunction especially among the middle and upper middle classes (often ridiculed by the rich and the poor in history for their sexual repression and ridiculousness...anxious, socially insecure people don't make good lovers), or otherwise to hysterical fits, nagging, petty jealousies, and reabsorption into the female muck of every day life; instead of romantic and idealistic flights of passion. Still I think the cause of why romantic passion has dried up is deeper and is possibly biological (feminism being only a reaction).
As to whether it is possible in movies, let's consider this. I know of only a couple of recent movies that can capture this well.