The way it works is this. Let's say you get 10 alerts one day about certain threads having new posts. You must view the new posts in all 10 threads in order to keep getting alerts about new posts them. In the event you only checked out the new posts in 6 of the 10 threads, you will only continue to get alerts in those 6 threads. You will not continue to get alerts in the 4 you neglected to revisit. So those 4 threads could continue to get new posts day after day but you wouldn't continue to get alerts about those posts.
It's done that way so you won't get a million alerts every day about every single post that is added to various threads. Instead, you're only getting alerts about the new posts in threads you're revisiting and staying on top of.