I'm not so sure Flech is right about the file not starting with a "From " line, I think it's just not starting with a "From ... 2003" line. The way I read what you're doing, you're using something like

while (<FILE>) {
  if (/^From .+ 2003/) {
    $mails[$#mails + 1] = $_;
  }
  else {
    $mails[$#mails] .= $_;
  }
    print $OUT, @mails;
}
[download]

The else tries to add lines to an array bin that the "From " test has not created, because it hasn't yet gotten to the section of the emails from 2003 that you want. Try something like

while (<FILE>) {
  if (/^From /) {
    if (/2003/ || $mailsStarted) {
      $mails[$#mails + 1] = $_;
      $mailsStarted = 1;
    }
  }
  elsif ( $mailsStarted ) {
    $mails[$#mails] .= $_;
  }
    print $OUT, @mails;
}
[download]

Note that you will get some non-2003 emails that come after the first 2003 email, but that should be ok.