Nope, not a bug… maybe, I’ll have to think about that.
Like I said each instance of the shortcode is not aware of any other on the page. Connections is primarily designed to be used on the page once. As you would find to be the case for other directory plugins too. I do provide enough configurable options to accomplish this though.
What you need to do is go to the Connections : Settings admin page, click the Display tab and disable the display search message option.