You've got a buffering problem. One option would be to set $/ to a reference to an integer, which will cause perl to give you a chunk of that many bytes on each read, rather than reading a line at a time. If you do this though, you then have to deal with assembling the records into lines yourself. Something like this should work...

open ( CORE, "/usr/bin/rsync $rsyncOPT --progress $outbox $inbox |" );
local $/ = \128; # read 128 bytes at a time
my $buffer = '';
while( <CORE> ) {
    $buffer .= $_;
    while ( $buffer =~ s/^(.*?)[\r\n]// ) {
        local $_ = $1;
        # code
    }
}
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Another (possibly better) option would be to use Expect, which is designed for this type of application...