I understand your dilemma; it is not an easy decision; I was in a similar position which concluded by a shutdown.
When searching on the Internet for information, your website comes out in the first page of the search result and provides the respective information in a generous and informative manner. Your website contains a lot of useful information. It even has a critic that I came across, which is healthy and is indicative that your site is known to the doggie community.
However, if the site does not at least support itself, then I believe that you should put 'Number One' first.
Is there a way for your site to get some sort of a sponsorship?