Your WordPress site looks to be hosted on whistle4democracycom.fatcow.com and all the paths within your web page use this domain.
However, the link you posted is to a different domain (whistle4democracy.org).
All gallery files must be hosted on the same domain or subdomain as the HTML page containing the gallery's JavaScript embedding code. This is due to the same-origin policy.

You should notice that clicking on the 'Uncategorized' button at the bottom reloads the page using the actual WordPress domain (whistle4democracycom.fatcow.com) which is the same as the domain used in the gallery's embedding code (which is why the gallery loads OK in this instance).

Possible solutions would be to try one of the following:

(1) Change your WordPress Address (URL) and/or Site Address (URL) in your WordPress settings ('Dashboard -> Settings -> General') to http://www.whistle4democracy.org

(2) Implement a Cross-Origin Resource Sharing (CORS) solution by adding the following line of code to the .htaccess file in the root directory of the domain which currently hosts your gallery (whistle4democracycom.fatcow.com).

Header add Access-Control-Allow-Origin "*"

If you would like to check whether your web server has all the features that Showkase needs, then please install and run the Showkase Server Compatibility Test .
If any of the tests fail, there are troubleshooting tips on the test's support page which may help.

Showkase has full support for Juicebox-Pro and the galleries could be created (and edited) from within the Showkase interface with no need for any manual coding at all.

If you would like to see what can be done with Showkase, please see the demo sites created with Showkase here.