Your problem is here...

$logfile="log.txt";
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and here...

if ($logfile =~ /$error/i) {
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Can you see?
You are trying to match the string "DOWN" against the string "log.txt". Of course, that will never match :)

I think you want:

while (my $line = <LOG>) {
    if ($line =~ /$error/i) {
    etc....
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Cheers,
Darren :)