This error appeared because you chose an extremely ineffective way—you call get_xpath on every element in the list instead of fetching all elements once.

The corected variant of your code:

#!/usr/bin/perl

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

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

$twig->parse(<<'XML');
<?xml version="1.0"?>
<article>
<label>here label for testing</label>
<fig id="fig001" position="float"><label>Fig. 1.</label><caption><p>fi
+rst</p></caption></fig>
<fig id="fig002" position="float"><label>Fig. 2.</label><caption><p>se
+cond</p></caption></fig>
<fig id="fig003" position="float"><label>Fig. 3.</label><caption><p>th
+ird</p></caption></fig>
<fig id="fig004" position="float"><label>Fig. 4.</label><caption><p>fo
+urth</p></caption></fig>
<fig id="fig005" position="float"><label>Fig. 5.</label><caption><p>fi
+fth</p></caption></fig>
<fig id="fig006" position="float"><label>Fig. 6.</label><caption><p>si
+xth</p></caption></fig>
</article>
XML

my $count = $twig->get_xpath('/article/fig//label'); 

for my $c (0..($count-1))
{
    my $t = $twig->get_xpath('/article/fig/label', 0);            #//f
+ig/label -here problem comes            
    my $pl = $twig->get_xpath('/article/fig//caption', $c);
    my $cut = $t->cut ;                             
    $cut->paste('first_child', $pl) ;                                 
+              

}

$twig->print;
[download]

The more efficient and clean way resulting in the same output:

#!/usr/bin/perl

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

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

$twig->parse(<<'XML');
<?xml version="1.0"?>
<article>
<label>here label for testing</label>
<fig id="fig001" position="float"><label>Fig. 1.</label><caption><p>fi
+rst</p></caption></fig>
<fig id="fig002" position="float"><label>Fig. 2.</label><caption><p>se
+cond</p></caption></fig>
<fig id="fig003" position="float"><label>Fig. 3.</label><caption><p>th
+ird</p></caption></fig>
<fig id="fig004" position="float"><label>Fig. 4.</label><caption><p>fo
+urth</p></caption></fig>
<fig id="fig005" position="float"><label>Fig. 5.</label><caption><p>fi
+fth</p></caption></fig>
<fig id="fig006" position="float"><label>Fig. 6.</label><caption><p>si
+xth</p></caption></fig>
</article>
XML

my @labels = $twig->get_xpath('/article/fig/label'); 
my @captions = $twig->get_xpath('/article/fig/caption');
for my $i (0..$#labels) {
    $labels[$i]->move('first_child', $captions[$i]);
}

$twig->print;
[download]

#!/usr/bin/perl

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

my $twig = new XML::Twig(
    twig_handlers => {
        '/article/fig' => sub {
            my $label = $_->first_child('label') or return;
            my $caption = $_->first_child('caption') or return;
            $label->move('first_child', $caption);
            $_->flush;
        }
},
    pretty_print => 'indented',                                     
);

$twig->parse(<<'XML');
<?xml version="1.0"?>
<article>
<label>here label for testing</label>
<fig id="fig001" position="float"><label>Fig. 1.</label><caption><p>fi
+rst</p></caption></fig>
<fig id="fig002" position="float"><label>Fig. 2.</label><caption><p>se
+cond</p></caption></fig>
<fig id="fig003" position="float"><label>Fig. 3.</label><caption><p>th
+ird</p></caption></fig>
<fig id="fig004" position="float"><label>Fig. 4.</label><caption><p>fo
+urth</p></caption></fig>
<fig id="fig005" position="float"><label>Fig. 5.</label><caption><p>fi
+fth</p></caption></fig>
<fig id="fig006" position="float"><label>Fig. 6.</label><caption><p>si
+xth</p></caption></fig>
</article>
XML

$twig->print;
[download]