Have you tried the regex I suggested?  Works for me:

my $tests = [
'Nov 29 16:01:27 
Nov 29 16:01:28 
Nov 29 16:01:28
Nov 29 16:01:28
Nov 29 16:01:22',

'Nov 29 16:01:27
Nov 29 16:01:28
Nov 29 16:01:28
Nov 29 16:01:28
Nov 30 16:01:22'
];

foreach my $test (@$tests) {
        if($test =~ qr/^((^|\n)Nov 29 [^\n]*)+$/s) {
             print "$test\n REGEX MATCHED\n";
        } else {
             print "$test\n FAILED!\n";
        }
}

__END__
Nov 29 16:01:27 
Nov 29 16:01:28 
Nov 29 16:01:28
Nov 29 16:01:28
Nov 29 16:01:22
 REGEX MATCHED

Nov 29 16:01:27
Nov 29 16:01:28
Nov 29 16:01:28
Nov 29 16:01:28
Nov 30 16:01:22
 FAILED!
[download]

Or modify ikegami's regex like this:

    qr/^(?:Nov 29 [^\n]*(\n|$))*\z/s
                        ^^^^^^
                        newline or end-of-line
[download]