Your description and your code are doing two very different things. Of course, that's why it's not doing what you want ;-)

You're looking for all directories that do not have a file "business_use.$node" in them, right? So, why not just do exactly that?

use File::Basename;
use File::Spec;

# grab the dirs.
my @dirs = grep { -d $_ } glob '/app/perform/workspace/htdocs/node_rep
+orts/*';

# look for any dirs that do not have the desired file in them.
my @missing_business_use_dirs = grep {
  # find the node name (it's the base name of the current directory)
  my $node = basename($_);
  # check if the desired file exists - keep the ones where it doesn't.
  not -e File::Spec->catfile($_, "business_use.$node");
} @dirs
[download]

Now @missing_business_use_dirs has your list of nodes.