Literally every forum that I frequent has this problem.
My solution is that I bookmark and visit the "watched threads" page instead of the home page. Repeated visits quickly bump that to the top of my browser's suggestions, so that (for example) if I type the letter T, the browser suggests https://titsintops.com/phpBB2/index.php?watched/threads
The recently updated threads are all listed first, and in bold type.
I would like just to add that this has happened to me, just today--the Tessa Fowler thread (which I have the alert on) didn't bother notifying me. I am puzzled, but I read this entire thread, and so I understand it may be glitchy software.
It's a pain to search in each page for unread threads, so I've just created a simple code to scrap unreaded threads from the website. Maybe you can find it helpful: