Two things.

First of all, XML is case-sensitive. appliance_list_output is not the same as APPLIANCE_LIST_OUTPUT, and the same goes for status and STATUS.

Second (after reading up on XPath), you're not getting results because you're only querying for the status attributes of APPLIANCE_LIST_OUTPUT nodes, as opposed to STATUS nodes descended from them. Try the following:

#!/usr/bin/perl

use feature qw/say/;
use XML::LibXML qw();

my $xml = XML::LibXML->load_xml(location => 'output.xml');

for ($xml->findnodes('//APPLIANCE_LIST_OUTPUT/descendant::STATUS/text(
+)')) {
    say;
}
[download]

Here's the output:

Online
Online
Online
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I've also used text() to select the text content of the status nodes, BTW. Leaving that out, you'd get "<STATUS>Online</STATUS>" for each node, rather than just "Online".

Does this do what you want?

BTW, here's a useful XPath tutorial site.