Are you by chance using Cloudflare for DNS? If so that would be the answer. Archive.is gives CF their own IP's back to them rather than the correct DNS answer on purpose. Some people will get endless captchas and some will get errors.
I switched Archive domains from Cloudflare DNS to Mullvad DNS on my unbound, haven’t had issues since. I also would recommend quad9 as a dns resolver, it doesn’t have an issue.
I think Archive doesn’t work with Apple’s private relay browsing feature due to them using Cloudflare for that capability, although I have not had time to test. Absolutely know it doesn’t work when using Cloudflare public DNS servers though.
It resolves for me but shows a captcha loop as others said, strangely the captcha page I'm getting seems to be some mockup of the Cloudflare one, using reCAPTCHA which Cloudflare publicly spoke about switching from.
Seems to be doing something odd, code of the page includes some XmlHttpRequest to a blog site with randomized query string (see end of https://pastebin.com/W21Au8RK), along with some fingerprint library (though commented out)
That blog site loads very slow for me if I go there manually - maybe some kind of DoS being directed to it?
Seen this same faux-cloudflare page used on btdig.com too, with the same strange XmlHttpRequest & fingerprint code, pretty weird.
The other day I was on hotel Wi-Fi and I got this recapture loop. I got off the Wi-Fi and went to mobile network and it came back. Are some ISPs blocking it ?
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.