I also started noticing this a few weeks ago. Scheduled posts were publishing, but the homepage, etc. was never being refreshed. 3 days of posts were not showing up, because the homepage was never being refreshed (though, I have cache timeout at 3600 seconds), which is still confusing....
I ended up turning on the option:
Clear all cache files when a post or page is published or updated
to fix this issue. Which it did, at the expense of clearing my whole cache, which is what I was having to do manually, to get new posts to show up.
But now, I'm having load issues, so I'm turning it back off.
Hopefully, I don't see the previous issue of the homepage never refreshing again.
If so, I will try to do as you say, and turn on the debug options and publish a test post...