The problem is the following:
Whenever someone leaves a comment on whichever post, the homepage cache is immediately flushed, by W3TC. That shouldn't happen until the cache expires, but it happens.
I'm not showing recent comments on the homepage and the content there is static, so to speak, in terms of comments.
I can't figure out what is the cause of this, but I need that page to stay cached for several hours at least, since it's the most visited page on the site. I suppose on every site.