"Giving up on playing a game" means a few different things to me.
Best case scenario, I give up on a game because I've played it too much. It's not a matter of it being essentially bad or boring, but I've just been through it too many times in a partiular period of time. This doesn't mean the game is bad (often the game is good!), but rather that it just isn't doing the job anymore for whatever reason and I need a break. But note that this can also lead to never really picking up the game again depending on circumstances. This latter one often depends on how much future updates really change the game. Still, this case is unique because I've usually played through all the content in the game at least once, up to a certain update's version of content.
Examples (for me) - Summertime Saga, SuperPowered, Legend of Queen Opala: Origins, Straitened Times, World After War, probably Loser pretty soon (been playing the betas since I support the game), Love & Vice, Dandy Boy Adventure, Amity Park.
Middleground: thse are games I've played like halfway through at time of writing and just gave up on without finishing them. This is actually a longer list of games than the above, but they don't tend to be as memorable. What makes this list unique is what I call the MrDots effect: great content, solid writing, but a desperate fear of actually getting to the point (in his game's case, creampieing and impregnating the daughter in Dating My Daughter). I give up because even though all the parts are good, there's just too much of a mouseclick barrier between me and sexytimes. Or the gameplay/story takes a sharp turn in the middle and I'm not with it.
Examples: Dating My Daughter (longwinded), Sunshine Love (longwinded, Lust Theory (I'm considering 2 an extension of 1. I finished AND enjoyed 1, but I can't really get into 2), The Company (longwinded AND a bit of a gameplay shift), College Daze (another story sharp turn), Mystwood Manor (I'm honestly trying again after a long hiatus, but there's something about how the mind control premise gets executed that feels a little too 'I shouldn't make this seem TOO non-con!' Might have been adjusted recently; often it's a matter of adding context to the seduction in between sex scenes rather than just a jarring shift from 'I hate you' to 'I love you,' but it's always been an issue there), Kronos Time Titan (I just get lost, honestly. Also it's weird enough to be interesting but janky enough to be frustrating), Aeon (this one's weird. It's...too polished? Yeah, kinda that. Also, there's so many girls so quickly seduced that even the good art doesn't overcome the encroaching 'meh' feeling), Willy D (same problem as before, same author as before).
Note: these games are often still great, and I still want to play them at some point, but it's much likelier that I never do and their development stops first rather than that I come back and finish them.
Updates too slow: sometimes Summertime Saga is in this category, but essentially this is just a genre where the updates take so long to come out that I straight up forget that a game exists.
Bad games: these are the ones I pick up and just kinda say 'ewww,' then put back down. Lots of easy tells here: awful writing in English, honey select art or just terrible custom art, author thinks they're funny and very much are not, gameplay is just too cumbersome to play, sex scenes simply aren't sexy, it's pushing a political/sexual politics agenda I can't get down with, it's very clearly a dev who's playing off the popularity of incest games but bakes very clearly into their game that incest is super forbidden because they're cowards or just the sad incestphobes who still want to make bank, or the premise is simply too wacky to be sexy in any sensible way. That last one is very case-by-case basis, because sometimes wacky is awesome (the Grey games are quite neat actually), but sometimes it goes just a little further and makes the game unsexy.
No surprise here, YMMV. And the last category is so vast I don't even bother remembering what games those are after I try them once.