He has never once claimed it gives somebody permanent immunity.
“Until they show me evidence that people who have already had the infection are dying in large numbers or being hospitalized or getting very sick, I just made my own personal decision that I’m not getting vaccinated because I’ve already had the disease and I have natural immunity,” Paul said."
Also, we know that many people have gotten COVID who have been vaccinated.
https://thehill.com/homenews/sunday-talk-shows/554918-rand-paul-im-not-getting-vaccinated