I have not noticed any recent changes in the way that the forum operates when it comes to keeping track of "new" posts. phpBB appears to automatically note when you have last logged in (and out) and does not place this in any browser cookie; at least none that I could find before.
At any time, if you explicitly or implicitly sign out (clicking the "Log out" link or changing your IP address), this will reset your "last visit" time and therefore what it will think are your "new" posts in the future. There's been more than one occasion when I've just signed on, seen dozens of new posts and then click the "Log out" link by accident, losing all of those "new" posts

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My technique is to click on the "View posts since last visit" link on the main forum index page, scroll back through as many pages as it takes to get to the end, and then launch separate browser tabs off of each thread I want to read, keeping the main listing intact and moving forward in time until I get to the top of the list. Then, even if my DSL connection locks up, I'll at least have a listing of those threads.
Of course I check in here many times during the day. If you don't visit all that often, then this may not work for you. And it certainly doesn't explain why you seem to be losing new posts right away.