I think one of the big issues is that the writers have tried to invest in new love interests but have rushed things too quickly, likely knowing that they wouldn't be on the book for long and editorial wouldn't enforce the next writer to follow through. Like, consider Shawn; it didn't take too damn long for them to go from "nice to meet you" to "I'd lose my mind if something happened to you!" There was no organic, natural build up and that left the whole thing feeling artificial and fake. No wonder fans didn't give a damn about her or her relationship with Dick. And this applies to pretty much every love interest introduced for any of the three characters; if the new love interest isn't just boring and bland to begin with, they don't get the time for the relationship to unfold properly.
If a new love interest is going to stick, then we need not only writers who will continue to build it up after the first guy leaves, we need editors who will enforce that consistency, and the love interest him/herself has to be compelling and interesting in their own right, and not just arm candy who exist solely for the protagonist's dramaz.
It's one of the reasons I've pushed for Power Girl so much. She's established as a character; we know who she is and what drives her as a individual, yet she isn't such a big deal she'd overshadow Dick. We know Karen Starr is Dick's type of girl, and she has history to draw from that can add to and enrich Nightwing's story, rather than just filling in as a requisite element of the genre. I've said all the same things about Kyle Rayner as a potential love interest for Kori; we know who Kyle is and can see how he and Kori could fit together and he exists as more than just a damsel for Kori to save. He's a character we're familiar and comfortable with, and not a new unknown factor.
Quality, as always, is the true problem here. DC has half assed their efforts regarding the love interests of these characters, but for a love interest to actually stick it requires real effort, time, and investment. And as we know, effort, time, and investment are the three things DC *isn't* willing to do with Nightwing, Starfire, and Babs (to a lesser extent).