There are different schemes for how signals and handlers behave. I think some of those schemes require that the signal handler redeclare itself as handling the signal:

sub killMyself {
    my( $sig )= @_;
    $SIG{$sig}= \&killMyself;
    if ($waitcoun­t > 6) {
        print STDERR "$serverNa­me ERROR:: The host is hosed\n";
        exit;
    }
    $waitcount­++;
}
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But I'm not certain. Could be worth a try until a better answer comes along?