Last night I noticed that my website’s had incorrect glue records at *.gtld-servers.net since probably mid-2012—which explains why a number of ISPs weren’t resolving it at all!
Paul Young explains what this means, and SmallClanger remarks in this ServerFault answer that it isn’t supposed to happen with modern software. The issue was probed using Squish and dig; and fixed by changing the nameservers listed at the registrar, forcing the glue records to be rewritten. Correctness was checked afterwards using whatsmydns.net.