Actually we are seeing the opposite to be true. Recent Israel data shows vaccine antibody counts can drop sharply in as early as 2-3 months: https://www.i24news.tv/en/news/coronavirus/1617185858-antibo...

Also, Most of the re-infected in Israel were from the vaccinated population, even after you adjust for vaccinated vs. unvaccinated population sizes: https://www.deseret.com/coronavirus/2021/7/20/22584134/whats...

On the other hand, with natural immunity, even after your antibody count wanes in your bloodstream, you still have your bone marrow and memory B cells to protect you:https://pubmed.ncbi.nlm.nih.gov/34030176/

It's looking more and more like natural immunity will be more long-lived than vaccine immunity: https://www.nature.com/articles/d41586-021-01442-9