I agree OP I'd like our relationships to keep going after the confirmation of intrest and pre/post love making and into DLCs as well. The LI should at least care for the hero if the hero is going off without them into a mission that would/could be dangerous, if the heros encountered something that should trouble their mental state like death and revial by space majic, personal trauma, or the loss of a close person, if the hero is captured and they have an LI that LI should be leading the search party and attempting to resuce him/her or at least in processess when things go crazy so when the hero meets up with the party and the hero asks why is the LI and the party even here the LI can respond they were petitioning the kIng (or so and so) to get men to find you when crap happened and they're relived to see you got out and expect all the details from you later tonight, or in contrast if the hero does things that should effect the LI negatively they should want to be harsh with the hero or lashout against them like oops I just made a move that would kill tons of people of your species LI or I know you like this thing/group/place/object and I just sold/killed/destroyed/or otherwise messed it up you should be mad or I know you're fighing a war with species X for a million years aaaand I just recruited it into our gang they should be ready to kill you and them.
One thing I loved in ME Leviathan DLC was if you romanced Tali she'll approch your diver suit alone and urge you to becareful in a meaningful way that little guesture assured me the game didn't forget (again) that we were well beyond trial stage and well into cometed she was worried for my male shep's life with out her looking out for him that was great. I wish however they went a step further after the shuttle ride and shep seeming to nearly die inside the LI and he could've had a moment in the main cabin where she's showing concern and curiosity over what happened giving the player the choice to tell her or to brush it off. If the player picks the former the player can vent, she can assure, comfort, or come up with solutions as lev's very existance in his head can affect himself, the war on both ally and enemy ends, and the future with the LI and allow their relationship to evolve again. Its just the hero's LI must show concern, confidence, or make vows to kill/save the hero if things go crazy.
I'd like the LI and the hero to have a give and take for concern addressing,encouragment, deescalations, and intrest in their lives/work/after game futures similar to how fshep and Garrus were it was a near perfect template for a relationship they both had problems that each took turns consoling eachother on or moments of showing support or fears then he took her on a date that was uniquly Garrus style no other LI could pull that off but Garrus if say Jacob did that it would be way off for him. I loved the date insert it was a the hero is stressed out like crazy so me as the boyfriend is going to give her at least one afternoon to not think about it, that was great each LI should have something that is uniquly their break from war moment with the player if they're more loving then something date like could occur if they're not affectionate in that manner then something that would apeal to them like say we have a emo character who isn't the cuddly type then maybe he/she says you know what lets go to a graveyard and scare the ravens (or something) it just needs to be something tied to the LI's persona and talents that can also be a romantic, fun, or qirky time to pause from the war or worries to have a bit of time with them trying to give their boyfriend/girlfriend the hero something else to be normal with.
Flirting or otherwise talking between the hero and the LI like in DAO would be nice as again as well those conversations between the npcs while we're just running around can be priceless especially when you're paring up people who don't like each other.