but the first time the script is run, the parameters are not saved, for every subsequent call to the script they are saved.

How are you checking?

#!/usr/bin/perl --

use strict;
use warnings;

use autodie;
use CGI;

use Shell::Command;

my $cgifile = __FILE__.'.txt';

{
    open my $out, '>', $cgifile;
    my $q = CGI->new({1..10});
    $q->save($out);
}

cat $cgifile;

{
    open my $in, '<', $cgifile;
    my $q = CGI->new($in);
    print $q->Dump;
}
__END__
1=2
3=4
7=8
9=10
5=6
=
<ul>
<li><strong>1</strong></li>
<ul>
<li>2</li>
</ul>
<li><strong>3</strong></li>
<ul>
<li>4</li>
</ul>
<li><strong>7</strong></li>
<ul>
<li>8</li>
</ul>
<li><strong>9</strong></li>
<ul>
<li>10</li>
</ul>
<li><strong>5</strong></li>
<ul>
<li>6</li>
</ul>
</ul>
[download]

Maybe its this bug #13158: empty name/value, when saved, prevents proper restore from filehandle.