The booming use of text-to-image generative models has raised concerns about their high risk of producing copyright-infringing content. While probabilistic copyright protection methods provide a probabilistic guarantee against such infringement, in this paper, we introduce Virtually Assured Amplification Attack (VA3), a novel online attack framework that exposes the vulnerabilities of these protection mechanisms. The proposed framework significantly amplifies the probability of generating infringing content on the sustained interactions with generative models and a non-trivial lower-bound on the success probability of each engagement. Our theoretical and experimental results demonstrate the effectiveness of our approach under various scenarios. These findings highlight the potential risk of implementing probabilistic copyright protection in practical applications of text-to-image generative models.