we go a long way back
So if you're a security conscious, you've configured your website to use the mozilla's Modern Configuarion through SSL Configuration Generator, which means minimum TLS 1.3
Unfortunately, the Internet Archive Wayback Machine, only looks back at history, not forward into modernity and doesn't support such newfangled security mechanisms.
Solution? temporarily degrade your security, TLS 1.2 should work as of 2020-04-30 while you make the wayback machine archive your site
if you have a sitemap, this oneliner should submit everything in it, 84 pages took ~230 secs.
1xargs -I '{}' -n 1 curl -Lv https://web.archive.org/save/'{}' < sitemap.txt