In theory, rebuttals play a vital role in the progression of science, pointing out flaws in published articles, and ensuring that science self-corrects. However, the effect of rebuttals has not been tested in practice. We examined seven high-profile original articles and their rebuttals, finding that original articles were cited 17 times more than rebuttals, and that annual citation numbers were unaffected by rebuttals. When citations did not mention rebuttals, 95% accepted the thesis of the original article uncritically, and support remained high over time. On the rare occasions when rebuttals were cited, the citing papers on average had neutral views of the original article, and 8% actually believed that the rebuttal agreed with the original article. Overall, only 5% of all citations were critical of the original paper. Our results point to an urgent need to change current publishing models to ensure that rebuttals are prominently linked to original articles.