A few thoughts.

• use strict; it keeps you out of trouble
• use warnings; it helps you diagnose errors
• use POSIX; it has a nice function strftime() that is very capable of formatting dates/times
• use LWP; keep perlish. There is no need for external programs, when there is a good module (LWP) for the same task.

I rewrote your program, to give you an idea what i mean.

use strict;
use warnings;

use LWP::Simple;
use POSIX qw(strftime);

my $address = $ARGV[0] or die "No address!";

# Create Router Re-Configuration script run command
my $rtr_cfg="wscript.exe rtr-telnet.vbs";

# Create a var that holds the html and fill it
my $html = get($address) || "";

# Create a Log File
open (fail_log,">>faillog.txt");

if ( $html =~ /<\/html>/)
{
    print fail_log strftime("%c - $address is up\n", localtime);
}
else
{
    print fail_log strftime("%c - $address is down\n", localtime);
    system ($rtr_cfg);
}
[download]

I made the address to check a parameter, so you can call that script like:

$ perl checksite.pl http://www.perlmonks.org
[download]

Update:
Added link to strftime reference for Win32

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