It's a bit weirder than that. It actually does save all the posts, but the "saved" page (like almost every other page on the site) will only show you 1000 items, so there's just no way to access all the older items once they've been "pushed off the end".
I posted some more information about it a while ago here: https://www.reddit.com/r/help/comments/7en0uu/my_saved_posts...