I'm wondering if you're complicating things a bit. Rather than count, and then loop, try simply looping. I have a suspicion that your cuts and pastes are changing the number of matches that //fig/label sees - once you've changed the first fig/label, it's no longer a fig/label. Try this:

#!/usr/bin/perl

use strict;
use warnings;
use XML::Twig;

my $twig = new XML::Twig(
                         pretty_print => 'record_c'
                        );

$twig->parsefile('1.xml');

for my $fig (
             $twig->get_xpath('//fig')
            )
{
    my $label   = $fig->get_xpath('./label', 0);
    my $caption = $fig->get_xpath('./caption', 0);

    next unless $label and $caption;

    $label->cut();
    $label->paste('first_child', $caption);

}

$twig->print;
[download]

That seems to do the trick. Also note the better variable names ;-)