Is there a better way I can do the (\d+\.\d+\.\d+\.\d+)? As you can tell, I'm just trying to match for a numeric IP address.

Take a look at Regexp::Common::net. Your code could be written as something like (untested code):

use Regexp::Common qw /net/;

# match dotted decimal IP address
# $1 = whole match, $2-5 = bytes
my $IP = $RE{net}{IPv4}{-keep};

foreach my $line (@connections) {
    if ($line =~ /^\s*$IP:\d+\s*->\s*$IP:\d+\s*->\s*$IP/x) {
       $client_ip{$1}{$iteration}++;
       $vips{$6}{$iteration}++;
       $frontend{$11}{$iteration}++;
    }
}
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Note that $IP will only match on legal decimal IP addresses (so 666.666.666.666 won't match). This may, or may not, be what you want ;-)