Without a little bit more of your code it's hard to say what's going wrong.
The following works just fine for me

#!/usr/bin/perl -w
use CGI;


open (IN, '</tmp/page.sav') or die qq(Failed to open input file);
my $page;
while (!eof(IN))
{
    $page = new CGI(IN);
}
close(IN);

print $page->header();
print $page->start_html();
print $page->startform(-method=>'POST');
$page->param(-name=>'name', -value=>'ColtsFoot');
print $page->textfield(-name=>'name', -value=>'$name');
print $page->submit(-name=>'submit', value=>'Submit');
print $page->endform();
print $page->end_html();

open (OUT, '>/tmp/page.sav') or die qq(Failed to open output file);
$page->save(OUT);
close(OUT);
[download]

The resulting file /tmp/page.sav looks like this

name=ColtsFoot
=
[download]

Hope this gives you a clue.