According to 17 USC § 507(b), one has three years in which to file a civil action for copyright infringement. If I were to chose to go after someone who infringed one of my copyrights during the past month, I would have until August, 2017, to file suit. Any DMCA notice would need to be sent a few weeks before the suit was filed.
If I take such action, it will be at a time of my choosing. I may not be in a hurry. Or I may wish to expedite a claim.
Some folks play chess. Some play checkers. But in both games one must play several moves ahead.
UPDATE—When I play cards, I often play with a deck missing the 3s and 7s. In fact, a pinochle deck lacks all the 2s, 4s, 5s, 6s, and 8s as well.