Ignoring the business side of it, let's take Halo for example, should Halo have stopped making games after Halo Reach?

I think it might have been better to do this because it would have left Halo in a ‘good stance’ for it's last game, feeling for the most part completed. Instead we got 2 more story lines on top of that that people aren't happy with compared to the original trilogy. I loved Halo 4,5, and Infinite, but I think I would have much better memories of Halo if they stopped after Reach.

I find that many popular game series want to go on forever, when it would have been better to stop after a few games and a finished story. Maybe there are ways around or ways to prolong the point when a series should stop. Let's again take Halo, what if we followed different people/teams for the stories in Halo 4-5 and Halo Infinite? I think that has the possibility to turn out better and prolong the point of when it should stop, although the constant risk of having to make entirely new stories with new people should be acknowledged.

I wonder if this is why Valve limits themselves to 2 games in a series, or follows the suggestion from the paragraph above.

Difficult question. I don't know about halo, but a series that is similar to me is Dead Space. 1 and 2 were extraordinary, but 3 was seriously underwhelming. Should they have stopped after 2? Not really, EA just should not have forced them to make an action game instead of a horror game. Did Dead Space 3 taint my memories of the other two? No, in actuality it made me appreciate them even more. And now that they made the superb Dead Space Remake, I can say even more so that they should not have stopped, but just adjusted their course.

I guess after a certain point a series might have lost its steam, but you just can stop following it. <Insert Game Series> doesn't get worse just because some 14 year old made a shitty fan-fic game about it, so why would it just because the “officials” made a game in the series that you no longer enjoy? I mean, you might feel that way, but I don't think thats something that a lot of people share. Take pokemon, which is a series that has been running for god know how long. Or World of Warcraft, where most people don't like the modern game but still hold the “classic” era in high regards and are playing it now that it has been re-released.

In the end, most/all big game companies care about money. They will keep a series alive for as long as possible. Even so, there might be people who enjoy the newer game, unless they are really low-effort or go against the series spirit. In eigther way, you should not let your own enjoyment or memories of a series be tainted by some newer entries that you don't like. Just don't buy the newer games, give em bad reviews if you think they suck, problem solved.

This is the same issue in many TV series.

Should they go on forever, or should they decide an ending point, and move on?

It's always a difficult call, but often it's all about community support. These companies have ways of measuring the audience.

As long as the new product moves something forward, why not?

“Say what you have to say, and then stop.”

It applies to all entertainment, not just book authors. There is no need to tie up all the loose ends, and often they help sell the world as an ongoing, real place that exists before the story and will continue after.

If the story is complete after one season, or after three, or after a single movie, or at some point in a game sequence, then be done.