This makes me think it's usually the connection timing out.
Normally when the auto-updater updates on a thread with no changes, it gets a short "http 304 not modified" message. When the thread gets new posts (including your own), the full thread html has to be downloaded. For large threads, it's larger and has a higher chance of timing out than others.
Requests launched when you manually refresh a page with F5 probably have a higher time-out value than AJAX requests, which would explain why refreshing would be more likely to fix it than hitting the update button again.
I have a few ideas on how to address this issue that I'll work on when I can.
I do notice sometimes after my browser (Firefox) has lost and re-gained an internet connection, I have to click on the "Update" button for it to actually work. I'm not really clear what's going on here, but I'm pretty sure it's something browser-side that stops AJAX from working on a page after so many failed requests until you interact with the page again in a certain way. This might explain some of your #3 issues specifically.