[StavrosK]

It turns out that some DNS servers cached the old nameservers and are now failing to resolve those. It's unfortunate, but all we can do is wait for the cache to expire :(

[contras1970]

Did you forget step 4 from https://cr.yp.to/djbdns/run-server.html#move-zone ?

[StavrosK]

No, it looks like Namecheap stops serving the old records when you change nameservers.