I'm relatively new to PerlMonks so I wasn't sure whether I should respond to the others' comments on this subject or not. The suggestions offered here were interesting and led to some useful information but did not solve the problem. However I did find a hokey way around this specific case. In this situation it appears that closing Word causes the $word object to point to invalid stuff and that is what seems to be causing the error messages. I experimented with various combinations and found that the following code bypasses the problem of the Perl script being terminated although there is still a warning message issued. The code that seems to work for this case is:

$icount = $word->Documents->Count();   
$done = 0;
while ($done == 0) {
    if ($word->Documents) {
        if (($mycnt = $word->Documents->Count()) != $icount) {
            $done = 1;
        }
    } else {
        undef $word;
        $word = Win32::OLE->GetActiveObjectord.Application')
             || Win32::OLE->new('Word.Application');
        $done = 1;
    }
    sleep 5;
}
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As I say, it's hokey but it seems to work for this specific case.