Last viewed post is tracked entirely server-side (ie, not in the browser). When you visit a page, an entry is made in a database that indicates the thread and presumably the last post or time viewed. Later when you visit the thread again, the server looks up the last viewed post in that thread and redirects the browser to the first new post.
There is little, if anything, the browser contributes to this process other than maintaining and presenting your identity to the server via a cookie. The fact that new threads show up in "My Flyertalk" when there are new posts means that FT is well aware of the last post you read and what the new post should be. But the new post redirection is failing.
The symptoms would seem to indicate that there is something server-side that is failing to redirect properly. Without any knowledge of FT's architecture, I would guess that a front end caching server somewhere is failing to keep up with new writes, but only the site engineers are in a position to confirm or rectify the issue.