"... I can't get the exact same regex to work ..."

That's a very poor problem report. In what way doesn't it work? Where's your expected and actual output? See "Short, Self-Contained, Correct Example".

With this code:

#!/usr/bin/env perl

use strict;
use warnings;

my $regexp='(?:Nameservers[^\n]*\n.*?)*(?>Hostname:\s+([\S]+)\n)';

my $resp = "

Domain:               myDomain.int
DNS:                  myDomain.int
Registered:           2013-05-17
Expires:              2023-05-31
Registration period:  1 year
VID:                  no
DNSSEC:               Unsigned delegation, DNSSEC disabled, no records
Status:               Active

Registrant
Handle:               ***N/A***
Name:                 myName Corp
Attention:            Reggie Person
Address:              SomeStreet 17
Postalcode:           numericZip
City:                 myCity
Country:              XX
Phone:                +12 34 56 78 90

Nameservers
Hostname:             ns1.dom.ext
Hostname:             ns2.dom.ext
Hostname:             ns3.dom.ext

";

my @caps = $resp =~ /$regexp/sg;
print "@caps\n";
[download]

I get this output:

ns1.dom.ext ns2.dom.ext ns3.dom.ext
[download]

The regex itself appears to be doing what you want. Perhaps the problem lies elsewhere — waiting to hear.