I have the impression that there's a dashboard that the admins use for "second chance" to allow them to schedule stories they think didn't do as well as expected, to give those stories a second (third?) bite at the cherry.
One sometimes sees suggestions from @dang to resubmit, and/or comments about giving stories another go around if they did worse than expected.
The only other manual intervention at that level I've heard of is to promote Ycombinator companies; but I'm not sure what complexion that takes.
There's possibly some manual actions around vouchs/flags, to revive comments that got flagged and have now been vouched for. Maybe it's all automated but I suspect there's judgement applied there; just based on how the site is run in general.
No particular insight, just been around here for ~15 years (eek!).
A simple way to refute this is to note that some links were posted multiple times and only got traction on the second or third time.