The HTML injected by the reCaptcha in PHP contains the following HTML for the reload button:
<a title="Get a new challenge" id="recaptcha_reload_btn"><img alt="Get a new challenge" src="http://www.google.com/recaptcha/api/img/red/refresh.gif" id="recaptcha_reload" height="17" width="25"></a>
This means you can add a Javascript event listener to the button and count the number of times it is clicked. This example uses jQuery to increment a global variable:
var recaptcha_reloaded = 0;
$(document).on("click", "#recaptcha_reload_btn", function() {
recaptcha_reloaded++;
});
How you send this information once it is captured is up to you. One possibility is injecting it into a hidden input field on a form before it is submitted.
Also note that this only counts the number of times the button was clicked, not the number of times it was actually reloaded. There is a delay between clicking the recaptcha reload button and when the recaptcha is actually reloaded, and additional clicks during this interval will be ignored.