A do-while loop should do the job without the goto:

my $output;
my $tries = 0;
do {
  $output = `expect -f show_running_config.exp $router->[$IP]`;
  if($?){     # subshell returns error
    $tries++; # count a try
    sleep 5;  # pause
  }
} while( $? and $tries < 4 ); # loop again if error and more tries
           # was the last try unsuccessful?
if($?){    # last try was an error, ran out of tries
  print "Unable to connect after $tries tries\n";
  exit;
}
# go on to handle the response in $output
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