close MSG;
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outside of the for loop just for aesthetic purposes and check for errors on your open statement:

open (MSG, ">>mailmessage") or die "File open failed: $!\n";
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/tmp/mailparser.pl < mail.message.file
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This suggests that you'll probably have to modify your procmail config line in some way, but I'm not familiar with procmail.

Update: I've had a similar problem using the /etc/aliases file to strip/redirect mail to a special account. I solved my problem by parsing the message and then resending it to a different account. This is sort of ugly, but it works until I can figure out the correct method:

#/etc/aliases entry

## The below entry saves an unaltered copy on account original, and
## pipes the incoming message through our program which 
## resends to the final destination account.  Be sure to execute
## 'newaliases' after you modify the /etc/aliases for the changed
## entry to be updated.

original: \original, "|/tmp/mailparser.pl"
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##
#  MboxParser stuff here
##

use MIME::Lite;
my $msg = new MIME::Lite
      To   => 'targetaccount@same.site.net',
      From => $from,
      Cc => $cc,
      Subject => $subject,
      Type => 'TEXT',
      Comments => $to,  ## save original to: if needed
      Data => $body_str;
MIME::Lite->send('smtp', "some.smtp.net", Timeout=>60);
$msg->send;
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--Jim