This happens if you use 1.1.1.1 as your DNS resolver, the result of a long-running dispute between Cloudflare and Archive.is[1]; searching HN for “archive cloudflare” will get you lots of discussion.
As I understand it: the technical cause is that the Archive.is authoritative DNS server refuses to respond correctly to requests without EDNS subnet information, and Cloudflare’s resolver refuses to send requests with it. (Cloudflare says this is for privacy reasons, and I believe Archive.is says their response is for legal reasons.) The captcha loop seems to be a recent development; apparently[2] it’s not actually from Cloudflare, just styled to look like it.
[1] https://jarv.is/notes/cloudflare-dns-archive-is-blocked/