You do undef $/, but where do you actually read the contents into $_?

Anyway, this works for me:

#!/usr/bin/perl
use strict;
use warnings;

$_ = do { local $/; <DATA> };

while ( /^(\d+-\d+-\d+(?:(?!\d+-\d+).)*keyword)(?:(?!\d+-\d+).)*?$/smg
+ ) {
      print "$1\n";
}

__DATA__
2008-10-01 message 1
2008-10-02 message 2
2008-10-03 multi-line message
         message 3 keyword
2008-10-04 message 4
2008-10-05 multi-line
         blah blah
         message 5 keyword junk
2008-10-06 message 6 blah keyword
2008-10-06 this is message 7
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