The Copyright Act of 1976 (Section 507) establishes a three-year period of the copyright owner to bring a claim of copyright infringement. This statute of limitations assumes that the copyright owner knew or should reasonably have known that the infringement occurred. Consequently, the three-year limitation begins when the owner learns about the infringement activity. Furthermore, the statute of limitations period does not start necessarily when the copyright owner first learns about the copyright infringement as long as the infringement is continuing. In these cases, the three-year period can begin at any time during the infringing activity. Thus, the statue of limitations only applies if 1) the copyright owner knew or should reasonable have known about the infringement activity, and 2) the infringement activity is not ongoing (i.e. has stopped).

As an illustrative example, we can consider the case of a student that photocopies his professor's textbook and uses it for his class. Let's assume that the professor knows that the student has photocopied his textbook and copyrighted materials. After finishing the course the students disposes of the copies. Since the infringing activity has stopped, he can only be successfully sued within the next three years. In the case that a lawsuit was filed against him after the statute of limitations period, he will be able to claim the plaintiff waited an unreasonable amount of time to bring the lawsuit.

References:
[1] Stim, R. "Intellectual Property. Patents, Trademarks, and Copyrights" West Legal Studies.
[2] Black's Law Dictionary 5th ed., (West Publishing, 1979).
[3] Copyright Act of 1976