You can do this a lot easier and shorter:

open my $tailf, "tail -f $logFile |" or die;

for (1,2) {
    my $line = '';
    $line = <$tailf> until $line =~ / on $ipaddress/;
    push @matches, $line;
}
[download]

(Okay, you'd have to include some check for eof so it won't get into an endless loop if the input is too short. But I won't change it because it's so nice and short :)