If an author doesn't plan to update a fic (because they lost interest, their life got more complicated, or whatever it is) they will say that. You’ll find a little “on hiatus” or a “this will never be finished” statement somewhere on the fic.
Those kind of announcements appear most often in the fic tags or summary, or sometimes on the author’s archive page, fic profile, etc. Most authors, when they put up a new story, also make a point to specify their posting schedule if they have one, or if they don’t stick to a set schedule, they'll usually give some indication of when they plan to update. I typically see that kind of statement in the author’s notes in the latest chapter.
But even if they didn’t tell you, guess what--we can reasonably assume that the answer to “when are we getting a new chapter” is always “as soon as I’m able to post one.”
There is almost never a need to ask when an update is coming.
If an author updates twice a week, for instance on Fridays and Mondays, and it’s Saturday... you don’t need to ask when the next chapter is coming, or to remind them to update soon. If it’s already Monday, and they haven’t posted yet? Wait until Tuesday. I can promise you, they did not forget. They have a good reason for the delay. Hurrying an author along will not make them happier or more willing to write.
Sometimes people are just curious and don’t mean to sound entitled. And most asks I’ve seen that amounted to “moar pls” were worded in a way that was far from rude or greedy. But understand, to a fic writer, a message that comes out of the blue asking when or if a new chapter is coming, can still feel like pressure. And to someone who’s probably already feeling the weight of life’s demands, that results in guilt, not inspiration.
So what does that mean, nobody can never ever express a desire to read further? Or ask about the next chapter in order to show an interest? Not at all! A statement like “I can’t wait to see what happens next!” is fine, as long as you also give some kind of response to the story that you’ve been given thus far. The author spent a long time writing the latest chapter, so if all the response they get is “OMG update soon! I need to know what happens!” it feels like you don’t care about what actually has happened in the fic.
What can you do if you just really, really need to know when you’re going to get your next fanfic fix? The best way is to encourage the author without pressuring them, because if they know that people enjoy the fic, they’ll be more likely to write more! In other words, couch your update ask in the context of feedback about the fic itself.
- Hi! I love your story so much. My favorite thing about it is XYZ. Just wondering, is there a tag I can track so that I don’t miss when the next update comes out? Thanks!
- Hi! I saw your note about your personal situation that put this fic on hold, and I just wanted to say I’m sorry that you’re going through that! The fic is one of my favorites, particularly the way that XYZ. Just curious, do you have an idea of when you might be able to come back to it? No pressure! Anyway, take care of yourself!
- Hi! Love your fic! I especially loved the line XYZ this chapter, it made me spittake all over my keyboard! I know you mentioned you wouldn’t be able to update anytime soon, so I was wondering if you could recommend anything else to read in the meantime? Thanks so much!
- Hi! Your fic is amazing! The part where XYZ was just the best. I noticed that you mentioned you planned to post on Wednesday, but I didn’t see a new chapter? Anyway, I subscribed now, so that I’ll know as soon as it comes out! And don’t worry if you need a few extra days, I know how life can be! Hope you’re having a good weekend!
- Hi! I know it’s been abandoned, but I just wanted to tell you that I really loved your fic, especially the scene where XYZ. I sometimes re-read that scene when I’m feeling down. Just wanted to let you know how much I appreciated it! Have a nice evening!
- Hi! I saw that you put your amazing fic on hiatus! I hope everything’s okay. You already know how much I love it from my comments and kudos, so I just wanted to reassure you that I’ll still be here whenever you can start posting again (and just for my own curiosity, any idea when that might be?) Thanks!
- Hi! I loved your fic, the way you characterized XYZ in particular! I’m definitely going to check out your other stuff to fill the time until it updates again! Just wondering, do you have a fic masterpost that lists all your work? Thanks and I'm excited to read more from you!
TL;DR: don’t pester fic authors for updates, give feedback on existing chapters, fic writers have lives and responsibilities so don’t be a dick