Why is my WordPress plugin abusing my API?

I've written a WordPress plugin that is available in the Plugins Repository from WordPress.org.

The plugin makes a widget available. The widget, when rendered, calls my public API, and caches the information it retrieves.

Here's the strange part. For the last few months, I've been getting blasted by a certain IP on the API. (multiple requests a second, when most valid requests are maybe one request an hour).

The strange thing is, my API doesn't give any valuable information for this request (it is basically sending an error message in JSON), it doesn't really effect my website (so probably not malicious), and they've kept it up for at least 5-6 months.

What could possibly cause a WordPress plugin to repeatedly load itself over and over? Or is there something I'm not considering?

EDIT

I don't think this is the case of a high traffic website - I doubt a website that is serving multiple pageviews a second has a broken widget on it - especially not a widget that is made primarily for non-profit organizations.

Also, the only thing my logs give me is the IP address of the server. I don't have any way of knowing what the website/domain is (at least, I don't think I can figure it out from the IP).