I found a couple older threads on this but thought I'd revive the idea to get some fresh perspectives.

If you have a player who is underperforming, when do you pull the plug on him during the season? Do you continue to ride him and trust in his real-life stats regardless, or do you accept he's headed for a bad season, for whatever reason, and drop him in the order or relegate him to the bench?

In my opinion, the only reason to make a change (be it in lineup placement or benching / waiving them) would be if you realized you made a mistake with your original drafting. I.e. if the theme is playing out differently than you expected. Even if that's true, you need to weigh the benefit that their potential replacement would bring against the sunk salary.

Every individual PA is an event independent from every other, and the results from prior PA in no way influence the results of any future PA. Dropping a player for a poor start makes no sense, unless as ozo said, that player is simply a poor fit for the theme or your strategy and was a mistake to begin with.

A player's performance is not in any way, ever, a pre-determined outcome.

Right, but if, say, a .330 real life hitter is hitting .250 after 100 SIM games, does that not suggest something may be off?

I get ozo's point, but we've all had that experience where a guy seems to be a perfect fit for what you're trying to do, but for whatever reason, he continues to underperform. Do you assume it's just prolonged bad luck? Do you assume there's something within the league or teams you're playing that's limiting him?

My expectations when drafting a team is to expect anamolies. How else to you explain Shoeless Joe Jackson (any year) out homering 1955 Willie Mays?

I'll admit that I'm relatively quick to adjust a lineup (almost never release someone) when a player is underperforming. In my head, I understand I set a lineup well based upon their real-life stats, but it just feels weird to have a guy batting .220/.280/.340 batting 3rd when the guy in the 8 spot is batting .320/.400/.450, or some other nonsense like that. Maybe there are some weird pitching matchups in my division that are contributing to this (lopsided L/R splits? super high/low BB pitchers?), and maybe it's completely luck, but it helps add to the realistic simulation feel of the game for me. If I'm 50+ games in and there are some really extreme anomalies in my lineup, I'll start tinkering.

In general if I can't figure out why the guy is struggling I'm not going to cut bait. If I drafted a guy primarily to steal bases and it turns out all 3 of my division mates and 5 other teams in the league have A+++ arm catchers, that might be a guy for whom it's worth taking the 10% WW hit to replace him with a better hitter. Base stealing's not working out. If I draft a lefty outfielder and the rotations in my division are 70% left-handed maybe I'll move on from that guy as well. If I draft a home run hitter and my division's full of nothing but deadballers, I'll almost certainly move on from some power bats. But if it continues to feel like an anomaly there's really no point at which I cut bait, because there's no reason to believe a less expensive replacement off the waiver wire is going to improve the situation. Or at the very least, if I haven't figured out why my player isn't working out, I don't know what to look for in terms of a replacement who could improve my situation. So even if it was a drafting "mistake" (bad luck, whatever), if I don't know what the mistake is I can't fix it. So I'll stick with the guy I have and not give up 10% of his price.