It is not an fd-limit issue. Using '>&=' reuses the file descriptor, so it is not increasing the number. You should probably show the whole strace output after the print of 'opened 4000 files'. Your parsing of strace may not be showing the system call actually triggering the die. Also, can you run:

#!/usr/bin/perl -w
use strict;
use Socket;

open OLDOUT, ">&STDOUT";
for (my $i=0;$i<3;$i++)
{
open STDOUT, ">&", \*OLDOUT or die "reset STDOUT - $!";
my ($in, $out);
my $buf;
open STDOUT, ">/dev/null" or die "redirect - $!";
socketpair( $in, $out, AF_UNIX, SOCK_STREAM, PF_UNSPEC) or die + $!;
printf STDERR "sock is $out file %d\n", fileno ($out);
open STDOUT, ">&=", fileno($out) or die ">&= fileno(fd) - $!";
print "test1\n";
open STDOUT, ">&=", $out or die ">&= fd - $!";
print "test2\n";

open STDOUT, ">&", \*OLDOUT or die "reset2 STDOUT - $!";
}
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It works OK for me, but I am using a 32-bit 5.8.6.