In Firefox settings, look for 'DNS'. For the "DNS over HTTPS" section, click the "Manage Exceptions" button, and manually add "archive.is", "archive.ph", "archive.today". Then restart the browser, and it might work.
That is what one would see if using Cloudflare DNS. It's cloudflare's captcha but archive.is is not on of their customers so it will just be a never-ending captcha.
archive.ph misreports its IP address when responding to queries from cloudflare, apparently on purpose. It's not too hard to dig up some old threads/comments discussing the issue if you're curious about the details--you can find A (The?) Cloudflare Guy discussing it from cloudflare's perspective here on HN, and The Archive.ph Guy tweeting about it from his perspective.
Archive.ph intentionally gives the wrong IP to requests from Cloudflare DNS servers, because cloudflare is not giving them information about the IP subnet that made the original DNS request, and archive.ph claims that is a massive problem for them.
It's a long standing well known thing for years now. For the technical details just google "archive.is cloudflare". It's been discussed and written up and explained many times over by now. Many times over right here on HN even.
I will only add that as far as I can tell, neither side is exactly doing anything wrong, other than the fact that they both could have concocted some sort of special handling for each other years ago if they wanted. The failure to bother is on both I think.