The statute of limitations applies separately to each instance of infringement, it doesn't start ticking at the first instance of infringement like you suggest.

The statute of limitations applies separately to each instance of infringement, it doesn't start ticking at the first instance of infringement like you suggest. For example if I hosted a copyrighted movie on my website for 3 years and happened to not get sued for it that doesn't mean I am in the clear to keep hosting that movie forever. Each time I make a copy of the movie to respond to a request is a separate instance of infringement and has its own statute of limitations. So Microsoft could still be sued for all the copies of the game they have distributed in the past 3 years.